The temperature (in degrees Fahrenheit) of food in a freezer is where is the time in

In Exercises 1–4, find the derivative of the function by using the definition of the derivative. \(f(x)=x^2-4x+6\) Text Transcription: f(x)=x^2 -4x+5

In Exercises 1–4, find the derivative of the function by using the definition of the derivative. \(f(x)=\sqrt{x}+1\) Text Transcription: f(x)=sqrtx +1

In Exercises 1–4, find the derivative of the function by using the definition of the derivative. \(f(x)=\frac{x+1}{x-1}\) Text Transcription: f(x)=x+1/x-1

In Exercises 1–4, find the derivative of the function by using the definition of the derivative. \(f(x)=\frac{6}{x}\) Text Transcription: f(x)=6/x

In Exercises 5 and 6, describe the x-values at which f is differentiable. \(f(x)=(x-3)^{2/5}\) Text Transcription: f(x)=(x-3)^2/5

In Exercises 5 and 6, describe the x-values at which f is differentiable. \(f(x)=\frac{3x}{x+1}\) Text Transcription: f(x)=3x/x+1

Sketch the graph of f(x) = 4 - | x - 2 |. (a) Is f continuous at x = 2? (b) Is f differentiable at x = 2? Explain.

Sketch the graph of \(f(x)=\left\{\begin{array}{ll} x^{2}+4 x+2, & x<-2 \\ 1-4 x-x^{2}, & x \geq-2 \end{array}\right.\) (a) Is f continuous at x = -2? (b) Is f differentiable at x = -2? Explain. Text Transcription: f(x)={x^2 +4x+2, x < -2 _ 1-4x-x^2 , x geq -2

In Exercises 9 and 10, find the slope of the tangent line to the graph of the function at the given point. \(g(x)=\frac{2}{3}x^2-\frac{x}{6},\ \ \ (-1,\ \frac{5}{6})\) Text Transcription: g(x)=2/3 x^2 - x/6 , (-1, 5/6 )

In Exercises 9 and 10, find the slope of the tangent line to the graph of the function at the given point. \(h(x)=\frac{3x}{8}-2x^2, \left(-2,-\frac{35}{4} \right)\) Text Transcription: h(x)=3x/8-2x^2, (-2,-35/4)

In Exercises 11 and 12, (a) find an equation of the tangent line to the graph of at the given point, (b) use a graphing utility to graph the function and its tangent line at the point, and (c) use the derivative feature of the graphing utility to confirm your results. \(f(x)=x^3-1\), (-1, -2) Text Transcription: f(x)=x^3-1

In Exercises 11 and 12, (a) find an equation of the tangent line to the graph of at the given point, (b) use a graphing utility to graph the function and its tangent line at the point, and (c) use the derivative feature of the graphing utility to confirm your results. \(f(x)=\frac{2}{x+1}\), (0, 2) Text Transcription: f(x)=2/x+1

In Exercises 13 and 14, use the alternative form of the derivative to find the derivative at x = c (if it exists). \(g(x)=x^2(x-1)\), c = 2 Text Transcription: g(x)=x^2(x-1)

In Exercises 13 and 14, use the alternative form of the derivative to find the derivative at x = c (if it exists). \(f(x)=\frac{1}{x+4}\), c = 3 Text Transcription: f(x)=1/x+4

In Exercises 15–30, use the rules of differentiation to find the derivative of the function. y = 25

In Exercises 15–30, use the rules of differentiation to find the derivative of the function. y = -30

In Exercises 15–30, use the rules of differentiation to find the derivative of the function. \(f(x)=x^8\) Text Transcription: f(x)=x^8

In Exercises 15–30, use the rules of differentiation to find the derivative of the function. \(g(x)=x^{20}\) Text Transcription: g(x)=x^20

In Exercises 15–30, use the rules of differentiation to find the derivative of the function. \(h(t)=13 t^{4}\) Text Transcription: h(t)=13t^4

In Exercises 15–30, use the rules of differentiation to find the derivative of the function. \(f(t)=-8 t^{5}\) Text Transcription: f(t)=-8t^5

In Exercises 15–30, use the rules of differentiation to find the derivative of the function. \(f(x)=x^{3}-11 x^{2}\) Text Transcription: f(x)=x^3-11x^2

In Exercises 15–30, use the rules of differentiation to find the derivative of the function. \(g(s)=4 s^{4}-5 s^{2}\) Text Transcription: g(s)=4s^4-5s^2

In Exercises 15–30, use the rules of differentiation to find the derivative of the function. \(h(x)=6 \sqrt{x}+3 \sqrt[3]{x}\) Text Transcription: h(x)=6 sqrt x+3 cube root x

In Exercises 15–30, use the rules of differentiation to find the derivative of the function. \(f(x)=x^{1 / 2}-x^{-1 / 2}\) Text Transcription: f(x)=x^1/2-x^-1/2

In Exercises 15–30, use the rules of differentiation to find the derivative of the function. \(g(t)=\frac{2}{3 t^{2}}\) Text Transcription: g(t)=2/3t^2

In Exercises 15–30, use the rules of differentiation to find the derivative of the function. \(h(x)=\frac{10}{(7 x)^{2}}\) Text Transcription: h(x)=10/7x^2

In Exercises 15–30, use the rules of differentiation to find the derivative of the function. \(f(\theta)=4 \theta-5 \sin \theta\) Text Transcription: f(theta)=4 theta-5 sin theta

In Exercises 15–30, use the rules of differentiation to find the derivative of the function. \(g(\alpha)=4 \cos \alpha+6\) Text Transcription: g(alpha)=4 cos alpha+6

In Exercises 15–30, use the rules of differentiation to find the derivative of the function. \(f(\theta)=3 \cos \theta-\frac{\sin \theta}{4}\) Text Transcription: f(theta)=3 cos theta-sin theta/4

In Exercises 15–30, use the rules of differentiation to find the derivative of the function. \(g(\alpha)=\frac{5 \sin \alpha}{3}-2 \alpha\) Text Transcription: g(alpha)=5 sin alpha/3-2 alpha

Writing In Exercises 31 and 32, the figure shows the graphs of a function and its derivative. Label the graphs as or and write a short paragraph stating the criteria you used in making your selection. To print an enlarged copy of the graph, go to the website www.mathgraphs.com.

Writing In Exercises 31 and 32, the figure shows the graphs of a function and its derivative. Label the graphs as or and write a short paragraph stating the criteria you used in making your selection. To print an enlarged copy of the graph, go to the website www.mathgraphs.com.

Vibrating String When a guitar string is plucked, it vibrates with a frequency of \(F=200 \sqrt T\) where F is measured in vibrations per second and the tension T is measured in pounds. Find the rates of change of F when (a) T = 4 and (b) T = 9. Text Transcription: F=200 sqrt T

Vertical Motion A ball is dropped from a height of 100 feet. One second later, another ball is dropped from a height of 75 feet. Which ball hits the ground first?

Vertical Motion To estimate the height of a building, a weight is dropped from the top of the building into a pool at ground level. How high is the building if the splash is seen 9.2 seconds after the weight is dropped?

Vertical Motion A bomb is dropped from an airplane at an altitude of 14,400 feet. How long will it take for the bomb to reach the ground? (Because of the motion of the plane, the fall will not be vertical, but the time will be the same as that for a vertical fall.) The plane is moving at 600 miles per hour. How far will the bomb move horizontally after it is released from the plane?

Projectile Motion A thrown ball follows a path described by \(y=x-0.02x^2\) (a) Sketch a graph of the path. (b) Find the total horizontal distance the ball is thrown. (c) At what x-value does the ball reach its maximum height? (Use the symmetry of the path.) (d) Find an equation that gives the instantaneous rate of change of the height of the ball with respect to the horizontal change. Evaluate the equation at x = 0, 10, 25, 30, and 50. (e) What is the instantaneous rate of change of the height when the ball reaches its maximum height? Text Transcription: y=x-0.02x^2

Projectile Motion The path of a projectile thrown at an angle of with level ground is \(y=x-\frac{32}{v_0^2}(x^2)\) where the initial velocity is \(v_0\) feet per second. (a) Find the x-coordinate of the point where the projectile strikes the ground. Use the symmetry of the path of the projectile to locate the x-coordinate of the point where the projectile reaches its maximum height. (b) What is the instantaneous rate of change of the height when the projectile is at its maximum height? (c) Show that doubling the initial velocity of the projectile multiplies both the maximum height and the range by a factor of 4. (d) Find the maximum height and range of a projectile thrown with an initial velocity of 70 feet per second. Use a graphing utility to graph the path of the projectile. Text Transcription: y=x-32/v_0^2(x^2) v_0

Horizontal Motion The position function of a particle moving along the x-axis is \(x(t)=t^2-3t+2\) for \(-\infty<t<\infty\). (a) Find the velocity of the particle. (b) Find the open t-interval(s) in which the particle is moving to the left. (c) Find the position of the particle when the velocity is 0. (d) Find the speed of the particle when the position is 0. Text Transcription: x(t)=t^2-3t+2 -infty<t<infty

Modeling Data The speed of a car in miles per hour and the stopping distance in feet are recorded in the table. (a) Use the regression capabilities of a graphing utility to find a quadratic model for the data. (b) Use a graphing utility to plot the data and graph the model. (c) Use a graphing utility to graph dy/dx. (d) Use the model to approximate the stopping distance at a speed of 65 miles per hour. (e) Use the graphs in parts (b) and (c) to explain the change in stopping distance as the speed increases.

In Exercises 41–54, find the derivative of the function. \(f(x)=\left(5 x^{2}+8\right)\left(x^{2}-4 x-6\right)\) Text Transcription: f(x)=(5x^2+8)(x^2-4x-6)

In Exercises 41–54, find the derivative of the function. \(g(x)=\left(x^{3}+7 x\right)(x+3)\) Text Transcription: g(x)=(x^3+7x)(x+3)

In Exercises 41–54, find the derivative of the function. \(h(x)=\sqrt{x} \sin x\) Text Transcription: h(x)=sqrt x sin x

In Exercises 41–54, find the derivative of the function. \(f(t)=2 t^{5} \cos t\) Text Transcription: f(t)=2t^5 cos t

In Exercises 41–54, find the derivative of the function. \(f(x)=\frac{x^{2}+x-1}{x^{2}-1}\) Text Transcription: f(x)=x^2+x-1/x^2-1

In Exercises 41–54, find the derivative of the function. \(f(x)=\frac{6 x-5}{x^{2}+1}\) Text Transcription: f(x)=6x-x^2+1

In Exercises 41–54, find the derivative of the function. \(f(x)=\frac{1}{9-4 x^{2}}\) Text Transcription: f(x)=1/9-4x^2

In Exercises 41–54, find the derivative of the function. \(f(x)=\frac{9}{3 x^{2}-2 x}\) Text Transcription: f(x)=9/3x^2-2x

In Exercises 41–54, find the derivative of the function. \(y=\frac{x^{4}}{\cos x}\) Text Transcription: y=x^4/cos x

In Exercises 41–54, find the derivative of the function. \(y=\frac{\sin x}{x^{4}}\) Text Transcription: y=sin x/x^4

In Exercises 41–54, find the derivative of the function. \(y=3x^2 \sec x\) Text Transcription: y=3x^2 sec x

In Exercises 41–54, find the derivative of the function. \(y=2x-x^2 \tan x\) Text Transcription: y=2x-x^2 tan x

In Exercises 41–54, find the derivative of the function. y = x cos x - sin x

In Exercises 41–54, find the derivative of the function. \(g(x)=3x \sin x + x^2 \cos x\) Text Transcription: g(x)=3x sin x + x^2 cos x

In Exercises 55–58, find an equation of the tangent line to the graph of f at the given point. \(f(x)=\frac{2 x^{3}-1}{x^{2}}\), (1, 1) Text Transcription: f(x)=2x^3-1/x^2

In Exercises 55–58, find an equation of the tangent line to the graph of f at the given point. \(f(x)=\frac{x+1}{x-1}, \quad\left(\frac{1}{2},-3\right)\) Text Transcription: f(x)=x+1/x-1, (1/2, -3)

In Exercises 55–58, find an equation of the tangent line to the graph of f at the given point.

In Exercises 55–58, find an equation of the tangent line to the graph of f at the given point. \(f(x)=\frac{1+\cos x}{1-\cos x}, \quad\left(\frac{\pi}{2}, 1\right)\) Text Transcription: f(x)=1+cos x/1-cos x, (pi/2,1)

Acceleration The velocity of an object in meters per second is \(v(t)=36-t^{2}, 0 \leq t \leq 6\). Find the velocity and acceleration of the object when t = 4. Text Transcription: v(t)=36-t^2, 0 <= t <= 6

Acceleration The velocity of an automobile starting from rest is \(v(t)=\frac{90 t}{4 t+10}\) where v is measured in feet per second. Find the vehicle's velocity and acceleration at each of the following times. (a) 1 second (b) 5 seconds (c) 10 seconds Text Transcription: v(t)=90t/4t+10

In Exercises 61– 66, find the second derivative of the function. \(g(t)=-8 t^{3}-5 t+12\) Text Transcription: g(t)=-8t^3-5t+12

In Exercises 61– 66, find the second derivative of the function. \(h(x)=21 x^{-3}+3 x\) Text Transcription: h(x)=21x^-3+3x

In Exercises 61– 66, find the second derivative of the function. \(f(x)=15 x^{5 / 2}\) Text Transcription: f(x)=15x^5/2

In Exercises 61– 66, find the second derivative of the function. \(f(x)=20 \sqrt[5]{x}\) Text Transcription: f(x)=20 5th root x

In Exercises 61– 66, find the second derivative of the function. \(f(\theta)=3 \tan \theta\) Text Transcription: f(theta)=3 tan theta

In Exercises 61– 66, find the second derivative of the function. h(t) = 10 cos t - 15 sin t

In Exercises 67 and 68, show that the function satisfies the equation. Function Equation y = 2 sin x + 3 cos x \(y^{\prime \prime}+y=0\) Text Transcription: y’’+y=0

In Exercises 67 and 68, show that the function satisfies the equation. Function Equation y=\frac{10-\cos x}{x} \(xy^\prime+y=\sin x\) Text Transcription: y=10-cos x/x xy’+y=sin x

In Exercises 69-80, find the derivative of the function. \(h(x)=\left(\frac{x+5}{x^{2}+3}\right)^{2}\) Text Transcription: h(x)=(x+5/x^2+3)^2

In Exercises 69-80, find the derivative of the function. \(f(x)=\left(x^{2}+\frac{1}{x}\right)^{5}\) Text Transcription: f(x)=(x^2+1/x)^5

In Exercises 69-80, find the derivative of the function. \(f(s)=\left(s^{2}-1\right)^{5 / 2}\left(s^{3}+5\right)\) Text Transcription: f(s)=(s^2-1)^5/2(s^3+5)

In Exercises 69-80, find the derivative of the function. \(h(\theta)=\frac{\theta}{(1-\theta)^{3}}\) Text Transcription: h(theta)=theta/(1-theta)^3

In Exercises 69-80, find the derivative of the function. y = 5 cos(9x + 1)

In Exercises 69-80, find the derivative of the function. \(y=1-\cos 2 x+2 \cos ^{2} x\) Text Transcription: y=1-cos 2x+2 cos^2 x

In Exercises 69-80, find the derivative of the function. \(y=\frac{x}{2}-\frac{\sin 2 x}{4}\) Text Transcription: y=x/2-sin 2x/4

In Exercises 69-80, find the derivative of the function. \(y=\frac{\sec ^{7} x}{7}-\frac{\sec ^{5} x}{5}\) Text Transcription: y=sec^7x/7-sec^5x/5

In Exercises 69-80, find the derivative of the function. \(y=\frac{2}{3} \sin ^{3 / 2} x-\frac{2}{7} \sin ^{7 / 2} x\) Text Transcription: y=2/3 sin^3/2 x - 2/7 sin^7/2 x

In Exercises 69-80, find the derivative of the function. \(f(x)=\frac{3 x}{\sqrt{x^{2}+1}}\) Text Transcription: f(x)=3x/sqrt x^2+1

In Exercises 69-80, find the derivative of the function. \(y=\frac{\sin \pi x}{x+2}\) Text Transcription: y=sin pi x/x+2

In Exercises 69-80, find the derivative of the function. \(y=\frac{\cos (x-1)}{x-1}\) Text Transcription: y=cos(x-1)/x-1

In Exercises 81– 84, find the derivative of the function at the given point. \(f(x)=\sqrt{1-x^{3}}\), (-2, 3) Text Transcription: f(x)=sqrt 1-x^3

In Exercises 81– 84, find the derivative of the function at the given point. \(f(x)=\sqrt[3]{x^{2}-1}\), (3, 2) Text Transcription: f(x)=cube root x^2-1

In Exercises 81– 84, find the derivative of the function at the given point. \(y=\frac{1}{2} \csc 2 x, \quad\left(\frac{\pi}{4}, \frac{1}{2}\right)\) Text Transcription: y=1/2 csc 2x, (pi/4, 1/2)

In Exercises 81– 84, find the derivative of the function at the given point. y = csc 3 x+ cot 3x, \(\left(\frac{\pi}{6}, 1\right)\) Text Transcription: (pi/6, 1)

In Exercises 85– 88, use a computer algebra system to find the derivative of the function. Use the utility to graph the function and its derivative on the same set of coordinate axes. Describe the behavior of the function that corresponds to any zeros of the graph of the derivative. \(g(x)=\frac{2 x}{\sqrt{x+1}}\) Text Transcription: g(x)=2x/sqrt x+1

In Exercises 85– 88, use a computer algebra system to find the derivative of the function. Use the utility to graph the function and its derivative on the same set of coordinate axes. Describe the behavior of the function that corresponds to any zeros of the graph of the derivative. \(f(x)=[(x-2)(x+4)]^{2}\) Text Transcription: f(x)=[(x-2)(x+4)]^2

In Exercises 85– 88, use a computer algebra system to find the derivative of the function. Use the utility to graph the function and its derivative on the same set of coordinate axes. Describe the behavior of the function that corresponds to any zeros of the graph of the derivative. \(f(t)=\sqrt{t+1} \sqrt[3]{t+1}\) Text Transcription: f(t)=sqrt t+1 cube root t+1

In Exercises 85– 88, use a computer algebra system to find the derivative of the function. Use the utility to graph the function and its derivative on the same set of coordinate axes. Describe the behavior of the function that corresponds to any zeros of the graph of the derivative. \(y=\sqrt{3 x}(x+2)^{3}\) Text Transcription: y= sqrt 3x(x+2)^3

In Exercises 89–92, (a) use a computer algebra system to find the derivative of the function at the given point, (b) find an equation of the tangent line to the graph of the function at the point, and (c) graph the function and its tangent line on the same set of coordinate axes. \(f(t)=t^{2}(t-1)^{5}\), (2,4) Text Transcription: f(t)=t^2(t-1)^5

In Exercises 89–92, (a) use a computer algebra system to find the derivative of the function at the given point, (b) find an equation of the tangent line to the graph of the function at the point, and (c) graph the function and its tangent line on the same set of coordinate axes. \(g(x)=x \sqrt{x^{2}+1}, \quad(3,3 \sqrt{10})\) Text Transcription: g(x)=x sqrt x^2+1, (3, 3 sqrt 10)

In Exercises 89–92, (a) use a computer algebra system to find the derivative of the function at the given point, (b) find an equation of the tangent line to the graph of the function at the point, and (c) graph the function and its tangent line on the same set of coordinate axes. \(f(x)=\tan \sqrt{1-x}, \quad(-2, \tan \sqrt{3})\) Text Transcription: f(x)=tan sqrt 1-x,(-2, tan sqrt 3)

In Exercises 89–92, (a) use a computer algebra system to find the derivative of the function at the given point, (b) find an equation of the tangent line to the graph of the function at the point, and (c) graph the function and its tangent line on the same set of coordinate axes. \(f(x)=2 \csc ^{3}(\sqrt{x}), \quad\left(1,2 \csc ^{3} 1\right)\) Text Transcription: f(x)= 2 csc^3(sqrt x), (1,2 csc^3 1)

In Exercises 93–96, find the second derivative of the function. \(y=7x^2+\cos 2x\) Text Transcription: y=7x^2+cos 2x

In Exercises 93–96, find the second derivative of the function. \(y=\frac{1}{x}+\tan x\) Text Transcription: y=1/x+tan x

In Exercises 93–96, find the second derivative of the function. f(x) = cot x

In Exercises 93–96, find the second derivative of the function. \(y=\sin^2x\) Text Transcription: y=sin^2x

In Exercises 97–100, use a computer algebra system to find the second derivative of the function. \(f(t)=\frac{4 t^{2}}{(1-t)^{2}}\) Text Transcription: f(t)=4t^2/(1-t)^2

In Exercises 97–100, use a computer algebra system to find the second derivative of the function. \(g(x)=\frac{6 x-5}{x^{2}+1}\) Text Transcription: g(x)=6x-5/x^2+1

In Exercises 97–100, use a computer algebra system to find the second derivative of the function. \(g(\theta)=\tan 3 \theta-\sin (\theta-1)$ 100. $h(x)=5 x \sqrt{x^{2}-16}\) Text Transcription: g(theta) = tan 3 theta - sin(theta-1)

In Exercises 97–100, use a computer algebra system to find the second derivative of the function. \(h(x)=5x\sqrt{x^2-16}\) Text Transcription: h(x)=5x sqrt x^2-16

Refrigeration The temperature T (in degrees Fahrenheit) of food in a freezer is \(T=\frac{700}{t^{2}+4 t+10}\) where t is the time in hours. Find the rate of change of T with respect to t at each of the following times. (a) t = 1 (b) t = 3 (c) t = 5 (d) t = 10 Text Transcription: T=700/t^2+4t+10

Fluid Flow The emergent velocity v of a liquid flowing from a hole in the bottom of a tank is given by \(v=\sqrt{2 g h}\), where g is the acceleration due to gravity (32 feet per second per second) and h is the depth of the liquid in the tank. Find the rates of change of v with respect to h when (a) h = 9 and (b) h = 4. (Note that g = +32 feet per second per second. The sign of g depends on how a problem is modeled. In this case, letting g be negative would produce an imaginary value for v.) Text Transcription: v=sqrt 2gh

In Exercises 103–108, find by dy/dx implicit differentiation. \(x^{2}+3 x y+y^{3}=10\) Text Transcription: x^2+3xy+y^3=10

In Exercises 103–108, find by dy/dx implicit differentiation. \(y^{2}=(x-y)\left(x^{2}+y\right)\) Text Transcription: y^2=(x-y)(x^2+y)

In Exercises 103–108, find by dy/dx implicit differentiation. \(\sqrt{x y}=x-4 y\) Text Transcription: sqrt xy=x-4y

In Exercises 103–108, find by dy/dx implicit differentiation. \(y \sqrt{x}-x \sqrt{y}=25\) Text Transcription: y sqrt x-x sqrt y= 25

In Exercises 103–108, find by dy/dx implicit differentiation. x sin y = y cos x

In Exercises 103–108, find by dy/dx implicit differentiation. cos(x + y) = x

In Exercises 109 and 110, find the equations of the tangent line and the normal line to the graph of the equation at the given point. Use a graphing utility to graph the equation, the tangent line, and the normal line. \(x^2+y^2=10\), (3, 1) Text Transcription: x^2+y^2=10

In Exercises 109 and 110, find the equations of the tangent line and the normal line to the graph of the equation at the given point. Use a graphing utility to graph the equation, the tangent line, and the normal line. \(x^2-y^2=20\), (6, 4) Text Transcription: x^2-y^2=20

A point moves along the curve \(y=\sqrt{x}\) in such a way that the y-value is increasing at a rate of 2 units per second. At what rate is x changing for each of the following values? (a) \(x=\frac{1}{2}\) (b) x = 1 (c) x = 4 Text Transcription: y = sqrt x x=1/2

Surface Area The edges of a cube are expanding at a rate of 8 centimeters per second. How fast is the surface area changing when each edge is 6.5 centimeters?

Depth The cross section of a five-meter trough is an isosceles trapezoid with a two-meter lower base, a three-meter upper base, and an altitude of 2 meters. Water is running into the trough at a rate of 1 cubic meter per minute. How fast is the water level rising when the water is 1 meter deep?

Linear and Angular Velocity A rotating beacon is located 1 kilometer off a straight shoreline (see figure). If the beacon rotates at a rate of 3 revolutions per minute, how fast (in kilometers per hour) does the beam of light appear to be moving to a viewer who is \(\frac{1}{2}\) kilometer down the shoreline? Text Transcription: 1/2

Moving Shadow A sandbag is dropped from a balloon at a height of 60 meters when the angle of elevation to the sun is \(30^{\circ}\) (see figure). Find the rate at which the shadow of the sandbag is traveling along the ground when the sandbag is at a height of 35 meters. [Hint: The position of the sandbag is given by \(s(t)=60-4.9 t^{2}\). ] Text Transcription: 30^o s(t)=60-4.9t^2