 4.4.1: Does j(x) ~ x 3 + 2x + tan x have aoy local maximum or minimum. val...
 4.4.2: Does g(x) ~ csex + 2 cotx have aoy local maximum values? Give reaso...
 4.4.3: Does j(x) ~ (7 + x)(11  3X)1/3 have an absolute minimum value? An ...
 4.4.4: Find values of a and b such that the function has a local extreme v...
 4.4.5: The greatest integer functioo j(x) ~ l x J, defmed for all values o...
 4.4.6: Give an example of a differentiable functioo j whose fIrst derivati...
 4.4.7: The functioo y ~ I/x does not take 00 either a maximum or a minimum...
 4.4.8: What are the maximum and minimum values of the function y ~ Ix I on...
 4.4.9: A graph that is large enough to show a functioo's global behavior m...
 4.4.10: (Continuation of Exercise 9.) .. Graph j(x) ~ (x'/8)  (2/5)x'  5x...
 4.4.11: Show that g(l) ~ sin2 1  31 decreases 00 every interval in its dom...
 4.4.12: Show that y ~ tan 8 increases 00 every interval in its domain. b. I...
 4.4.13: Show that the equatioo x' + 2x2  2 ~ 0 has exactly ooe solution on...
 4.4.14: Show that j(x) ~ x/(x + I) increases on every interval in its domai...
 4.4.15: As a result of a heavy rain, the volume of water in a reservoir inc...
 4.4.16: The formula F(x) ~ 3x + C gives a different function for each value...
 4.4.17: Show that even though x I x+I"x+I' Doesn't this contradict Coro11a...
 4.4.18: Calculate the ftrst derivatives of f(x) ~ x'/(x' + I) and g(x) ~ I...
 4.4.19: In Exercises 19 and 20, use the graph to answer the questions
 4.4.20: In Exercises 19 and 20, use the graph to answer the questions
 4.4.21: Each of the graphs in Exercises 21 and 22 is the graph of the posit...
 4.4.22: Each of the graphs in Exercises 21 and 22 is the graph of the posit...
 4.4.23: Graph the curves in Exercises 2332. Y ~ x'  (x'/6)
 4.4.24: Graph the curves in Exercises 2332. .y~x'3x'+3
 4.4.25: Graph the curves in Exercises 2332. y~ x'+6x'9x+3
 4.4.26: Graph the curves in Exercises 2332. Y ~ (l/8)(x' + 3x'  9x  27)
 4.4.27: Graph the curves in Exercises 2332. 27
 4.4.28: Graph the curves in Exercises 2332. y ~ x'(2x'  9)
 4.4.29: Graph the curves in Exercises 2332. Y ~ x  3x'/3
 4.4.30: Graph the curves in Exercises 2332. y ~ XI/3(X  4)
 4.4.31: Graph the curves in Exercises 2332. 1.y~x~
 4.4.32: Graph the curves in Exercises 2332. 2.y~x~
 4.4.33: Each of Exercises 3338 gives the first derivative of a function y ...
 4.4.34: Each of Exercises 3338 gives the first derivative of a function y ...
 4.4.35: Each of Exercises 3338 gives the first derivative of a function y ...
 4.4.36: Each of Exercises 3338 gives the first derivative of a function y ...
 4.4.37: Each of Exercises 3338 gives the first derivative of a function y ...
 4.4.38: Each of Exercises 3338 gives the first derivative of a function y ...
 4.4.39: In Exercises 3942, graph each function. Then use the function's ft...
 4.4.40: In Exercises 3942, graph each function. Then use the function's ft...
 4.4.41: In Exercises 3942, graph each function. Then use the function's ft...
 4.4.42: In Exercises 3942, graph each function. Then use the function's ft...
 4.4.43: Sketch the graphs of the rational functions in Exercises 4350. _x...
 4.4.44: Sketch the graphs of the rational functions in Exercises 4350. ,y...
 4.4.45: Sketch the graphs of the rational functions in Exercises 4350. y~x
 4.4.46: Sketch the graphs of the rational functions in Exercises 4350. x'...
 4.4.47: Sketch the graphs of the rational functions in Exercises 4350. y 2x
 4.4.48: Sketch the graphs of the rational functions in Exercises 4350. y~,
 4.4.49: Sketch the graphs of the rational functions in Exercises 4350. Y ...
 4.4.50: Sketch the graphs of the rational functions in Exercises 4350. y~...
 4.4.51: The sum of two nonnegative numbers is 36. Find the numbers if a. th...
 4.4.52: The sum of two nonnegative numbers is 36. Find the numbers if a. th...
 4.4.53: An isosceles triangle has its vertex at the origin and its base par...
 4.4.54: A customer has asked you to design an opentop rectangular stainles...
 4.4.55: Find the height and radius of the largest right circular cylinder t...
 4.4.56: The figure here shows two right circular cones, one upside down ins...
 4.4.57: Your company can manufacture x hundred grade A tires and y hundred ...
 4.4.58: The positions of two particles on the saxis are SI = cos t and S2 ...
 4.4.59: An opentop rectangular box is constructed from a lOin.by16in. ...
 4.4.60: What is the approximate length (in feet) of the longest ladder you ...
 4.4.61: Let f(x) = 3x  x3. Show that the equation f(x) = 4 has a solution...
 4.4.62: Let f(x) = x4  x3. Show that the equation f(x) = 75 has a solution...
 4.4.63: Find the indefinite integrals (most general antiderivatives) in Exe...
 4.4.64: Find the indefinite integrals (most general antiderivatives) in Exe...
 4.4.65: Find the indefinite integrals (most general antiderivatives) in Exe...
 4.4.66: Find the indefinite integrals (most general antiderivatives) in Exe...
 4.4.67: Find the indefinite integrals (most general antiderivatives) in Exe...
 4.4.68: Find the indefinite integrals (most general antiderivatives) in Exe...
 4.4.69: Find the indefinite integrals (most general antiderivatives) in Exe...
 4.4.70: Find the indefinite integrals (most general antiderivatives) in Exe...
 4.4.71: Find the indefinite integrals (most general antiderivatives) in Exe...
 4.4.72: Find the indefinite integrals (most general antiderivatives) in Exe...
 4.4.73: Find the indefinite integrals (most general antiderivatives) in Exe...
 4.4.74: Find the indefinite integrals (most general antiderivatives) in Exe...
 4.4.75: Find the indefinite integrals (most general antiderivatives) in Exe...
 4.4.76: Find the indefinite integrals (most general antiderivatives) in Exe...
 4.4.77: Find the indefinite integrals (most general antiderivatives) in Exe...
 4.4.78: Find the indefinite integrals (most general antiderivatives) in Exe...
 4.4.79: Solve the initial value problems in Exercises 79 82. dx =~' y(I) = 1
 4.4.80: Solve the initial value problems in Exercises 79 82. 80
 4.4.81: Solve the initial value problems in Exercises 79 82. d2r r 3 81. ...
 4.4.82: Solve the initial value problems in Exercises 79 82. d3r 82. 3 = ...
Solutions for Chapter 4: Applications of Derivatives
Full solutions for Thomas' Calculus  12th Edition
ISBN: 9780321587992
Solutions for Chapter 4: Applications of Derivatives
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Thomas' Calculus, edition: 12. Since 82 problems in chapter 4: Applications of Derivatives have been answered, more than 5194 students have viewed full stepbystep solutions from this chapter. Thomas' Calculus was written by and is associated to the ISBN: 9780321587992. Chapter 4: Applications of Derivatives includes 82 full stepbystep solutions.

Arithmetic sequence
A sequence {an} in which an = an1 + d for every integer n ? 2 . The number d is the common difference.

Binomial
A polynomial with exactly two terms

Binomial probability
In an experiment with two possible outcomes, the probability of one outcome occurring k times in n independent trials is P1E2 = n!k!1n  k2!pk11  p) nk where p is the probability of the outcome occurring once

Compounded continuously
Interest compounded using the formula A = Pert

Constant function (on an interval)
ƒ(x 1) = ƒ(x 2) x for any x1 and x2 (in the interval)

Cotangent
The function y = cot x

Dihedral angle
An angle formed by two intersecting planes,

Firstdegree equation in x , y, and z
An equation that can be written in the form.

Horizontal component
See Component form of a vector.

Intercepted arc
Arc of a circle between the initial side and terminal side of a central angle.

Inverse properties
a + 1a2 = 0, a # 1a

Modulus
See Absolute value of a complex number.

Piecewisedefined function
A function whose domain is divided into several parts with a different function rule applied to each part, p. 104.

Polar distance formula
The distance between the points with polar coordinates (r1, ?1 ) and (r2, ?2 ) = 2r 12 + r 22  2r1r2 cos 1?1  ?22

Power regression
A procedure for fitting a curve y = a . x b to a set of data.

Radian
The measure of a central angle whose intercepted arc has a length equal to the circle’s radius.

Rectangular coordinate system
See Cartesian coordinate system.

Right triangle
A triangle with a 90° angle.

Symmetric difference quotient of ƒ at a
ƒ(x + h)  ƒ(x  h) 2h

Variation
See Power function.