 4.1: Explain the difference between an absolute maximum and a local maxi...
 4.2: (a) What does the Extreme Value Theorem say? (b) Explain how the Cl...
 4.3: (a) State Fermats Theorem. (b) Define a critical number of f.
 4.4: (a) State Rolles Theorem. (b) State the Mean Value Theorem and give...
 4.5: (a) State the Increasing/Decreasing Test. (b) What does it mean to ...
 4.6: (a) State the First Derivative Test. (b) State the Second Derivativ...
 4.7: (a) What does lHospitals Rule say? (b) How can you use lHospitals R...
 4.8: State whether each of the following limit forms is indeterminate. W...
 4.9: If you have a graphing calculator or computer, why do you need calc...
 4.10: (a) Given an initial approximation x1 to a root of the equation fsx...
 4.11: (a) What is an antiderivative of a function f ? (b) Suppose F1 and ...
 4.12: Determine whether the statement is true or false. If it is true, ex...
 4.13: Determine whether the statement is true or false. If it is true, ex...
 4.14: Determine whether the statement is true or false. If it is true, ex...
 4.15: Determine whether the statement is true or false. If it is true, ex...
 4.16: Determine whether the statement is true or false. If it is true, ex...
 4.17: Determine whether the statement is true or false. If it is true, ex...
 4.18: Determine whether the statement is true or false. If it is true, ex...
 4.19: Determine whether the statement is true or false. If it is true, ex...
 4.20: Determine whether the statement is true or false. If it is true, ex...
 4.21: Determine whether the statement is true or false. If it is true, ex...
 4.22: Use the guidelines of Section 4.5 to sketch the curve. y x 1 2 x 2
 4.23: Use the guidelines of Section 4.5 to sketch the curve. y 1 xsx 2 3d 2
 4.24: Use the guidelines of Section 4.5 to sketch the curve. y 1 x 2 2 1 ...
 4.25: Use the guidelines of Section 4.5 to sketch the curve. y sx 2 1d 3 x 2
 4.26: Use the guidelines of Section 4.5 to sketch the curve.y s1 2 x 1 s1...
 4.27: Use the guidelines of Section 4.5 to sketch the curve. y xs2 1 x
 4.28: Use the guidelines of Section 4.5 to sketch the curve. y x 2y3 sx 2...
 4.29: Use the guidelines of Section 4.5 to sketch the curve.y ex sin x, 2...
 4.30: Use the guidelines of Section 4.5 to sketch the curve.y 4x 2 tan x,...
 4.31: Use the guidelines of Section 4.5 to sketch the curve. y sin21 s1yxd
 4.32: Use the guidelines of Section 4.5 to sketch the curve. y e2x2x 2
 4.33: Use the guidelines of Section 4.5 to sketch the curve.y sx 2 2de2x
 4.34: Use the guidelines of Section 4.5 to sketch the curve.y x 1 lnsx 2 ...
 4.35: Produce graphs of f that reveal all the important aspects of the cu...
 4.36: Produce graphs of f that reveal all the important aspects of the cu...
 4.37: Produce graphs of f that reveal all the important aspects of the cu...
 4.38: Produce graphs of f that reveal all the important aspects of the cu...
 4.39: Graph f sxd e 21yx2 in a viewing rectangle that shows all the main ...
 4.40: (a) Graph the function fsxd 1ys1 1 e 1yx d. (b) Explain the shape o...
 4.41: Use the graphs of f, f9, and f 0 to estimate the xcoordinates of t...
 4.42: Use the graphs of f, f9, and f 0 to estimate the xcoordinates of t...
 4.43: Investigate the family of functions fsxd lnssin x 1 Cd. What featur...
 4.44: Investigate the family of functions fsxd cxe2cx 2 . What happens to...
 4.45: Show that the equation 3x 1 2 cos x 1 5 0 has exactly one real root.
 4.46: Suppose that f is continuous on f0, 4g, fs0d 1, and 2 < f9sxd < 5 f...
 4.47: By applying the Mean Value Theorem to the function fsxd x 1y5 on th...
 4.48: For what values of the constants a and b is s1, 3d a point of infle...
 4.49: Let tsxd fsx 2 d, where f is twice differentiable for all x, f9sxd ...
 4.50: Find two positive integers such that the sum of the first number an...
 4.51: Show that the shortest distance from the point sx1, y1d to the stra...
 4.52: Find the point on the hyperbola xy 8 that is closest to the point s...
 4.53: Find the smallest possible area of an isosceles triangle that is ci...
 4.54: Find the volume of the largest circular cone that can be inscribed ...
 4.55: In DABC, D lies on AB, CD AB,  AD   BD  4 cm, and  CD  5 cm. ...
 4.56: Solve Exercise 55 when  CD  2 cm
 4.57: The velocity of a wave of length L in deep water is v K L C 1 C L w...
 4.58: A metal storage tank with volume V is to be constructed in the shap...
 4.59: A hockey team plays in an arena with a seating capacity of 15,000 s...
 4.60: A manufacturer determines that the cost of making x units of a comm...
 4.61: Use Newtons method to find the root of the equation x5 2 x4 1 3x2 2...
 4.62: Use Newtons method to find all solutions of the equation sin x x 2 ...
 4.63: Use Newtons method to find the absolute maximum value of the functi...
 4.64: Use the guidelines in Section 4.5 to sketch the curve y x sin x, 0 ...
 4.65: Find the most general antiderivative of the function. fsxd 4sx 2 6x...
 4.66: Find the most general antiderivative of the function. tsxd 1 x 1 1 ...
 4.67: Find the most general antiderivative of the function. fstd 2 sin t ...
 4.68: Find the most general antiderivative of the function. fsxd x23 1 co...
 4.69: Find f. f9std 2t 2 3 sin t, fs0d 5
 4.70: Find f. f9sud u2 1 su u , fs1d 3
 4.71: Find f. f 0sxd 1 2 6x 1 48x 2 , fs0d 1, f9s0d 2
 4.72: Find f. f 0sxd 5x 3 1 6x 2 1 2, fs0d 3, fs1d 22
 4.73: A particle is moving with the given data. Find the position of the ...
 4.74: A particle is moving with the given data. Find the position of the ...
 4.75: (a) If fsxd 0.1ex 1 sin x, 24 < x < 4, use a graph of f to sketch a...
 4.76: Investigate the family of curves given by fsxd x 4 1 x 3 1 cx 2 In ...
 4.77: A canister is dropped from a helicopter 500 m above the ground. Its...
 4.78: In an automobile race along a straight road, car A passed car B twi...
 4.79: A rectangular beam will be cut from a cylindrical log of radius 10 ...
 4.80: If a projectile is fired with an initial velocity v at an angle of ...
 4.81: If an electrostatic field E acts on a liquid or a gaseous polar die...
 4.82: If a metal ball with mass m is projected in water and the force of ...
 4.83: Show that, for x . 0, x 1 1 x 2 , tan21 x , x
 4.84: Sketch the graph of a function f such that f9sxd , 0 for all x, f 0...
 4.85: A light is to be placed atop a pole of height h feet to illuminate ...
 4.86: Water is flowing at a constant rate into a spherical tank. Let Vstd...
Solutions for Chapter 4: Applications of Differentiation
Full solutions for Single Variable Calculus: Early Transcendentals  8th Edition
ISBN: 9781305270336
Solutions for Chapter 4: Applications of Differentiation
Get Full SolutionsThis textbook survival guide was created for the textbook: Single Variable Calculus: Early Transcendentals, edition: 8. Single Variable Calculus: Early Transcendentals was written by and is associated to the ISBN: 9781305270336. This expansive textbook survival guide covers the following chapters and their solutions. Since 86 problems in chapter 4: Applications of Differentiation have been answered, more than 37460 students have viewed full stepbystep solutions from this chapter. Chapter 4: Applications of Differentiation includes 86 full stepbystep solutions.

Angular speed
Speed of rotation, typically measured in radians or revolutions per unit time

Arccosine function
See Inverse cosine function.

Characteristic polynomial of a square matrix A
det(xIn  A), where A is an n x n matrix

Convergence of a sequence
A sequence {an} converges to a if limn: q an = a

Coordinate plane
See Cartesian coordinate system.

Direct variation
See Power function.

Division
a b = aa 1 b b, b Z 0

Frequency table (in statistics)
A table showing frequencies.

Gaussian elimination
A method of solving a system of n linear equations in n unknowns.

Graphical model
A visible representation of a numerical or algebraic model.

Head minus tail (HMT) rule
An arrow with initial point (x1, y1 ) and terminal point (x2, y2) represents the vector <8x 2  x 1, y2  y19>

Horizontal shrink or stretch
See Shrink, stretch.

Integrable over [a, b] Lba
ƒ1x2 dx exists.

Limaçon
A graph of a polar equation r = a b sin u or r = a b cos u with a > 0 b > 0

Modified boxplot
A boxplot with the outliers removed.

Probability function
A function P that assigns a real number to each outcome O in a sample space satisfying: 0 … P1O2 … 1, P12 = 0, and the sum of the probabilities of all outcomes is 1.

Radicand
See Radical.

Semiminor axis
The distance from the center of an ellipse to a point on the ellipse along a line perpendicular to the major axis.

Solve an equation or inequality
To find all solutions of the equation or inequality

Solve by elimination or substitution
Methods for solving systems of linear equations.