 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 3492 students have viewed full stepbystep solutions from this chapter. Thomas' Calculus was written by Sieva Kozinsky and is associated to the ISBN: 9780321587992. Chapter 4: Applications of Derivatives includes 82 full stepbystep solutions.

Compound interest
Interest that becomes part of the investment

Damping factor
The factor Aea in an equation such as y = Aeat cos bt

End behavior asymptote of a rational function
A polynomial that the function approaches as.

Equivalent arrows
Arrows that have the same magnitude and direction.

Equivalent systems of equations
Systems of equations that have the same solution.

Exponential decay function
Decay modeled by ƒ(x) = a ? bx, a > 0 with 0 < b < 1.

Factor
In algebra, a quantity being multiplied in a product. In statistics, a potential explanatory variable under study in an experiment, .

Law of sines
sin A a = sin B b = sin C c

Limit at infinity
limx: qƒ1x2 = L means that ƒ1x2 gets arbitrarily close to L as x gets arbitrarily large; lim x: q ƒ1x2 means that gets arbitrarily close to L as gets arbitrarily large

Mathematical induction
A process for proving that a statement is true for all natural numbers n by showing that it is true for n = 1 (the anchor) and that, if it is true for n = k, then it must be true for n = k + 1 (the inductive step)

Natural exponential function
The function ƒ1x2 = ex.

Oddeven identity
For a basic trigonometric function f, an identity relating f(x) to f(x).

Order of an m x n matrix
The order of an m x n matrix is m x n.

Pascal’s triangle
A number pattern in which row n (beginning with n = 02) consists of the coefficients of the expanded form of (a+b)n.

Reference angle
See Reference triangle

Repeated zeros
Zeros of multiplicity ? 2 (see Multiplicity).

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

Terminal side of an angle
See Angle.

Variable (in statistics)
A characteristic of individuals that is being identified or measured.

Zero of a function
A value in the domain of a function that makes the function value zero.
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