 4.1: Does have any local maximum or minimum values? Give reasons for you...
 4.2: Does have any local maximum values? Give reasons for your answer.
 4.3: Does have an absolute minimum value? An absolute maximum? If so, fi...
 4.4: Find values of a and b such that the function has a local extreme v...
 4.5: Does have an absolute minimum value? An absolute maximum? If so, fi...
 4.6: Does have an absolute minimum value? An absolute maximum? If so, fi...
 4.7: In Exercises 7 and 8, find the absolute maximum and absolute minimu...
 4.8: In Exercises 7 and 8, find the absolute maximum and absolute minimu...
 4.9: The greatest integer function defined for all values of x, assumes ...
 4.10: a. Give an example of a differentiable function whose first derivat...
 4.11: The function does not take on either a maximum or a minimum on the ...
 4.12: What are the maximum and minimum values of the function on the inte...
 4.13: A graph that is large enough to show a functions global behavior ma...
 4.14: (Continuation of Exercise 13.) a. Graph over the interval Where doe...
 4.15: a. Show that decreases on every interval in its domain. b. How many...
 4.16: a. Show that increases on every interval in its domain. b. If the c...
 4.17: a. Show that the equation has exactly one solution on [0, 1]. b. Fi...
 4.18: a. Show that increases on every interval in its domain. b. Show tha...
 4.19: As a result of a heavy rain, the volume of water in a reservoir inc...
 4.20: The formula gives a different function for each value of C. All of ...
 4.21: Show that even though Doesnt this contradict Corollary 2 of the Mea...
 4.22: Calculate the first derivatives of and What can you conclude about ...
 4.23: In Exercises 23 and 24, use the graph to answer the questions
 4.24: In Exercises 23 and 24, use the graph to answer the questions
 4.25: Estimate the intervals on which the function is a. increasing. b. d...
 4.26: Estimate the intervals on which the function is a. increasing. b. d...
 4.27: Graph the curves in Exercises 2742.
 4.28: Graph the curves in Exercises 2742.
 4.29: Graph the curves in Exercises 2742.
 4.30: Graph the curves in Exercises 2742.
 4.31: Graph the curves in Exercises 2742.
 4.32: Graph the curves in Exercises 2742.
 4.33: Graph the curves in Exercises 2742.
 4.34: Graph the curves in Exercises 2742.
 4.35: Graph the curves in Exercises 2742.
 4.36: Graph the curves in Exercises 2742.
 4.37: Graph the curves in Exercises 2742.
 4.38: Graph the curves in Exercises 2742.
 4.39: Graph the curves in Exercises 2742.
 4.40: Graph the curves in Exercises 2742.
 4.41: Graph the curves in Exercises 2742.
 4.42: Graph the curves in Exercises 2742.
 4.43: Each of Exercises 4348 gives the first derivative of a function (a)...
 4.44: Each of Exercises 4348 gives the first derivative of a function (a)...
 4.45: Each of Exercises 4348 gives the first derivative of a function (a)...
 4.46: Each of Exercises 4348 gives the first derivative of a function (a)...
 4.47: Each of Exercises 4348 gives the first derivative of a function (a)...
 4.48: Each of Exercises 4348 gives the first derivative of a function (a)...
 4.49: In Exercises 4952, graph each function. Then use the functions firs...
 4.50: In Exercises 4952, graph each function. Then use the functions firs...
 4.51: In Exercises 4952, graph each function. Then use the functions firs...
 4.52: In Exercises 4952, graph each function. Then use the functions firs...
 4.53: Sketch the graphs of the rational functions in Exercises 5360.
 4.54: Sketch the graphs of the rational functions in Exercises 5360.
 4.55: Sketch the graphs of the rational functions in Exercises 5360.
 4.56: Sketch the graphs of the rational functions in Exercises 5360.
 4.57: Sketch the graphs of the rational functions in Exercises 5360.
 4.58: Sketch the graphs of the rational functions in Exercises 5360.
 4.59: Sketch the graphs of the rational functions in Exercises 5360.
 4.60: Sketch the graphs of the rational functions in Exercises 5360.
 4.61: Use lHpitals Rule to find the limits in Exercises 6172
 4.62: Use lHpitals Rule to find the limits in Exercises 6172
 4.63: Use lHpitals Rule to find the limits in Exercises 6172
 4.64: Use lHpitals Rule to find the limits in Exercises 6172
 4.65: Use lHpitals Rule to find the limits in Exercises 6172
 4.66: Use lHpitals Rule to find the limits in Exercises 6172
 4.67: Use lHpitals Rule to find the limits in Exercises 6172
 4.68: Use lHpitals Rule to find the limits in Exercises 6172
 4.69: Use lHpitals Rule to find the limits in Exercises 6172
 4.70: Use lHpitals Rule to find the limits in Exercises 6172
 4.71: Use lHpitals Rule to find the limits in Exercises 6172
 4.72: Use lHpitals Rule to find the limits in Exercises 6172
 4.73: Find the limits in Exercises 7384.
 4.74: Find the limits in Exercises 7384.
 4.75: Find the limits in Exercises 7384.
 4.76: Find the limits in Exercises 7384.
 4.77: Find the limits in Exercises 7384.
 4.78: Find the limits in Exercises 7384.
 4.79: Find the limits in Exercises 7384.
 4.80: Find the limits in Exercises 7384.
 4.81: Find the limits in Exercises 7384.
 4.82: Find the limits in Exercises 7384.
 4.83: Find the limits in Exercises 7384.
 4.84: Find the limits in Exercises 7384.
 4.85: The sum of two nonnegative numbers is 36. Find the numbers if a. th...
 4.86: The sum of two nonnegative numbers is 20. Find the numbers a. if th...
 4.87: An isosceles triangle has its vertex at the origin and its base par...
 4.88: A customer has asked you to design an opentop rectangular stainles...
 4.89: Find the height and radius of the largest right circular cylinder t...
 4.90: The figure here shows two right circular cones, one upside down ins...
 4.91: Your company can manufacture x hundred grade A tires and y hundred ...
 4.92: The positions of two particles on the saxis are and a. What is the...
 4.93: An opentop rectangular box is constructed from a 10in.by16in. ...
 4.94: What is the approximate length (in feet) of the longest ladder you ...
 4.95: Let Show that the equation has a solution in the interval [2, 3] an...
 4.96: Let Show that the equation has a solution in the interval [3, 4] an...
 4.97: Find the indefinite integrals (most general antiderivatives) in Exe...
 4.98: Find the indefinite integrals (most general antiderivatives) in Exe...
 4.99: Find the indefinite integrals (most general antiderivatives) in Exe...
 4.100: Find the indefinite integrals (most general antiderivatives) in Exe...
 4.101: Find the indefinite integrals (most general antiderivatives) in Exe...
 4.102: Find the indefinite integrals (most general antiderivatives) in Exe...
 4.103: Find the indefinite integrals (most general antiderivatives) in Exe...
 4.104: Find the indefinite integrals (most general antiderivatives) in Exe...
 4.105: Find the indefinite integrals (most general antiderivatives) in Exe...
 4.106: Find the indefinite integrals (most general antiderivatives) in Exe...
 4.107: Find the indefinite integrals (most general antiderivatives) in Exe...
 4.108: Find the indefinite integrals (most general antiderivatives) in Exe...
 4.109: Find the indefinite integrals (most general antiderivatives) in Exe...
 4.110: Find the indefinite integrals (most general antiderivatives) in Exe...
 4.111: Find the indefinite integrals (most general antiderivatives) in Exe...
 4.112: Find the indefinite integrals (most general antiderivatives) in Exe...
 4.113: Find the indefinite integrals (most general antiderivatives) in Exe...
 4.114: Find the indefinite integrals (most general antiderivatives) in Exe...
 4.115: Find the indefinite integrals (most general antiderivatives) in Exe...
 4.116: Find the indefinite integrals (most general antiderivatives) in Exe...
 4.117: Find the indefinite integrals (most general antiderivatives) in Exe...
 4.118: Find the indefinite integrals (most general antiderivatives) in Exe...
 4.119: Find the indefinite integrals (most general antiderivatives) in Exe...
 4.120: Find the indefinite integrals (most general antiderivatives) in Exe...
 4.121: Solve the initial value problems in Exercises 121124.
 4.122: Solve the initial value problems in Exercises 121124.
 4.123: Solve the initial value problems in Exercises 121124.
 4.124: Solve the initial value problems in Exercises 121124.
 4.125: Can the integrations in (a) and (b) both be correct? Explain
 4.126: Can the integrations in (a) and (b) both be correct? Explain
 4.127: The rectangle shown here has one side on the positive yaxis, one s...
 4.128: The rectangle shown here has one side on the positive yaxis, one s...
 4.129: In Exercises 129 and 130, find the absolute maximum and minimum val...
 4.130: In Exercises 129 and 130, find the absolute maximum and minimum val...
 4.131: In Exercises 131 and 132, find the absolute maxima and minima of th...
 4.132: In Exercises 131 and 132, find the absolute maxima and minima of th...
 4.133: Graph the following functions and use what you see to locate and es...
 4.134: Graph Does the function appear to have an absolute minimum value? C...
 4.135: Graph over Explain what you see
 4.136: A round underwater transmission cable consists of a core of copper ...
Solutions for Chapter 4: Applications of Derivatives
Full solutions for Thomas' Calculus Early Transcendentals  12th Edition
ISBN: 9780321588760
Solutions for Chapter 4: Applications of Derivatives
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Chapter 4: Applications of Derivatives includes 136 full stepbystep solutions. This textbook survival guide was created for the textbook: Thomas' Calculus Early Transcendentals, edition: 12. Since 136 problems in chapter 4: Applications of Derivatives have been answered, more than 2077 students have viewed full stepbystep solutions from this chapter. Thomas' Calculus Early Transcendentals was written by and is associated to the ISBN: 9780321588760.

Absolute maximum
A value ƒ(c) is an absolute maximum value of ƒ if ƒ(c) ? ƒ(x) for all x in the domain of ƒ.

Addition principle of probability.
P(A or B) = P(A) + P(B)  P(A and B). If A and B are mutually exclusive events, then P(A or B) = P(A) + P(B)

Addition property of inequality
If u < v , then u + w < v + w

Coordinate plane
See Cartesian coordinate system.

Directed distance
See Polar coordinates.

Halflife
The amount of time required for half of a radioactive substance to decay.

Invertible linear system
A system of n linear equations in n variables whose coefficient matrix has a nonzero determinant.

Linear function
A function that can be written in the form ƒ(x) = mx + b, where and b are real numbers

Linear programming problem
A method of solving certain problems involving maximizing or minimizing a function of two variables (called an objective function) subject to restrictions (called constraints)

Measure of center
A measure of the typical, middle, or average value for a data set

Negative association
A relationship between two variables in which higher values of one variable are generally associated with lower values of the other variable.

Permutations of n objects taken r at a time
There are nPr = n!1n  r2! such permutations

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

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

Recursively defined sequence
A sequence defined by giving the first term (or the first few terms) along with a procedure for finding the subsequent terms.

Sample standard deviation
The standard deviation computed using only a sample of the entire population.

Singular matrix
A square matrix with zero determinant

Square matrix
A matrix whose number of rows equals the number of columns.

xcoordinate
The directed distance from the yaxis yzplane to a point in a plane (space), or the first number in an ordered pair (triple), pp. 12, 629.

Zero vector
The vector <0,0> or <0,0,0>.
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