 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 11436 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.

Angle of depression
The acute angle formed by the line of sight (downward) and the horizontal

Coefficient
The real number multiplied by the variable(s) in a polynomial term

Directed angle
See Polar coordinates.

Eccentricity
A nonnegative number that specifies how offcenter the focus of a conic is

Equivalent equations (inequalities)
Equations (inequalities) that have the same solutions.

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

Higherdegree polynomial function
A polynomial function whose degree is ? 3

Independent variable
Variable representing the domain value of a function (usually x).

Linear inequality in x
An inequality that can be written in the form ax + b < 0 ,ax + b … 0 , ax + b > 0, or ax + b Ú 0, where a and b are real numbers and a Z 0

Logarithmic form
An equation written with logarithms instead of exponents

Multiplicative inverse of a complex number
The reciprocal of a + bi, or 1 a + bi = a a2 + b2 ba2 + b2 i

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

Phase shift
See Sinusoid.

Radicand
See Radical.

Random behavior
Behavior that is determined only by the laws of probability.

Reflection across the xaxis
x, y and (x,y) are reflections of each other across the xaxis.

Standard form: equation of a circle
(x  h)2 + (y  k2) = r 2

Symmetric matrix
A matrix A = [aij] with the property aij = aji for all i and j

Unit ratio
See Conversion factor.

Weights
See Weighted mean.