 3.1: Give the definition of a critical number, and graph a function show...
 3.2: Consider the odd function that is continuous and differentiable and...
 3.3: In Exercises 3 and 4, find the absolute extrema of the function on ...
 3.4: In Exercises 3 and 4, find the absolute extrema of the function on ...
 3.5: In Exercises 5 and 6, determine whether Rolles Theorem can be appli...
 3.6: In Exercises 5 and 6, determine whether Rolles Theorem can be appli...
 3.7: Consider the function (a) Graph the function and verify that (b) No...
 3.8: Can the Mean Value Theorem be applied to the function on the interv...
 3.9: In Exercises 912, find the point(s) guaranteed by the Mean Value Th...
 3.10: In Exercises 912, find the point(s) guaranteed by the Mean Value Th...
 3.11: In Exercises 912, find the point(s) guaranteed by the Mean Value Th...
 3.12: In Exercises 912, find the point(s) guaranteed by the Mean Value Th...
 3.13: For the function determine the value of guaranteed by the Mean Valu...
 3.14: Demonstrate the result of Exercise 13 for on the interval 3xy
 3.15: In Exercises 1518, find the critical numbers (if any) and the open ...
 3.16: In Exercises 1518, find the critical numbers (if any) and the open ...
 3.17: In Exercises 1518, find the critical numbers (if any) and the open ...
 3.18: In Exercises 1518, find the critical numbers (if any) and the open ...
 3.19: In Exercises 19 and 20, use the First Derivative Test to find any r...
 3.20: In Exercises 19 and 20, use the First Derivative Test to find any r...
 3.21: Harmonic Motion The height of an object attached to a spring is giv...
 3.22: Writing The general equation giving the height of an oscillating ob...
 3.23: In Exercises 23 and 24, determine the points of inflection and disc...
 3.24: In Exercises 23 and 24, determine the points of inflection and disc...
 3.25: In Exercises 25 and 26, use the Second Derivative Test to find all ...
 3.26: In Exercises 25 and 26, use the Second Derivative Test to find all ...
 3.27: Think About It In Exercises 27 and 28, sketch the graph of a functi...
 3.28: Think About It In Exercises 27 and 28, sketch the graph of a functi...
 3.29: Writing A newspaper headline states that The rate of growth of the ...
 3.30: Inventory Cost The cost of inventory depends on the ordering and st...
 3.31: Modeling Data Outlays for national defense (in billions of dollars)...
 3.32: Modeling Data The manager of a store recorded the annual sales (in ...
 3.33: In Exercises 33 40, find the limit. xy4
 3.34: In Exercises 33 40, find the limit. 4x
 3.35: In Exercises 33 40, find the limit. 4x2
 3.36: In Exercises 33 40, find the limit. 4x2
 3.37: In Exercises 33 40, find the limit. x20
 3.38: In Exercises 33 40, find the limit. x20y
 3.39: In Exercises 33 40, find the limit. 20y
 3.40: In Exercises 33 40, find the limit. 0y4
 3.41: In Exercises 4144, find any vertical and horizontal asymptotes of t...
 3.42: In Exercises 4144, find any vertical and horizontal asymptotes of t...
 3.43: In Exercises 4144, find any vertical and horizontal asymptotes of t...
 3.44: In Exercises 4144, find any vertical and horizontal asymptotes of t...
 3.45: In Exercises 4548, use a graphing utility to graph the function. Us...
 3.46: In Exercises 4548, use a graphing utility to graph the function. Us...
 3.47: In Exercises 4548, use a graphing utility to graph the function. Us...
 3.48: In Exercises 4548, use a graphing utility to graph the function. Us...
 3.49: In Exercises 4966, analyze and sketch the graph of the function. 3x...
 3.50: In Exercises 4966, analyze and sketch the graph of the function. xy...
 3.51: In Exercises 4966, analyze and sketch the graph of the function. 210xy
 3.52: In Exercises 4966, analyze and sketch the graph of the function. 10xy4
 3.53: In Exercises 4966, analyze and sketch the graph of the function. 10...
 3.54: In Exercises 4966, analyze and sketch the graph of the function. xy4y
 3.55: In Exercises 4966, analyze and sketch the graph of the function. 4yx
 3.56: In Exercises 4966, analyze and sketch the graph of the function. 4yx3
 3.57: In Exercises 4966, analyze and sketch the graph of the function. yx3
 3.58: In Exercises 4966, analyze and sketch the graph of the function. x3x
 3.59: In Exercises 4966, analyze and sketch the graph of the function. x3xy
 3.60: In Exercises 4966, analyze and sketch the graph of the function. 3xy2
 3.61: In Exercises 4966, analyze and sketch the graph of the function. xy2
 3.62: In Exercises 4966, analyze and sketch the graph of the function. xy2x
 3.63: In Exercises 4966, analyze and sketch the graph of the function. y2x3
 3.64: In Exercises 4966, analyze and sketch the graph of the function. 2x3
 3.65: In Exercises 4966, analyze and sketch the graph of the function. x34
 3.66: In Exercises 4966, analyze and sketch the graph of the function. x34x
 3.67: Find the maximum and minimum points on the graph of (a) without usi...
 3.68: Consider the function for positive integer values of (a) For what v...
 3.69: Distance At noon, ship is 100 kilometers due east of ship Ship is s...
 3.70: Maximum Area Find the dimensions of the rectangle of maximum area, ...
 3.71: Minimum Length A right triangle in the first quadrant has the coord...
 3.72: Minimum Length The wall of a building is to be braced by a beam tha...
 3.73: Maximum Area Three sides of a trapezoid have the same length Of all...
 3.74: Maximum Area Show that the greatest area of any rectangle inscribed...
 3.75: Distance Find the length of the longest pipe that can be carried le...
 3.76: Distance Rework Exercise 75, given corridors of widths meters and m...
 3.77: Distance A hallway of width 6 feet meets a hallway of width 9 feet ...
 3.78: Length Rework Exercise 77, given that one hallway is of width meter...
 3.79: Minimum Cost In Exercises 79 and 80, find the speed in miles per ho...
 3.80: Minimum Cost In Exercises 79 and 80, find the speed in miles per ho...
 3.81: In Exercises 81 and 82, use Newtons Method to approximate any real ...
 3.82: In Exercises 81 and 82, use Newtons Method to approximate any real ...
 3.83: In Exercises 83 and 84, use Newtons Method to approximate, to three...
 3.84: In Exercises 83 and 84, use Newtons Method to approximate, to three...
 3.85: In Exercises 85 and 86, find the differential 2xx
 3.86: In Exercises 85 and 86, find the differential xx2
 3.87: Surface Area and Volume The diameter of a sphere is measured to be ...
 3.88: Demand Function A company finds that the demand for its commodity i...
 3.1: Graph the fourthdegree polynomial for various values of the consta...
 3.2: (a) Graph the fourthdegree polynomial for 0, 1, 2, and 3. For what...
 3.3: Let Determine all values of the constant such that has a relative m...
 3.4: (a) Let be a quadratic polynomial. How many points of inflection do...
 3.5: Prove Darbouxs Theorem: Let be differentiable on the closed interva...
 3.6: Let and be functions that are continuous on and differentiable on ....
 3.7: Prove the following Extended Mean Value Theorem. If and are continu...
 3.8: (a) Let . Find and Show that for small values of the difference is ...
 3.9: The amount of illumination of a surface is proportional to the inte...
 3.10: Consider a room in the shape of a cube, 4 meters on each side. A bu...
 3.11: The line joining and crosses the two parallel lines, as shown in th...
 3.12: The figures show a rectangle, a circle, and a semicircle inscribed ...
 3.13: (a) Prove that (b) Prove that (c) Let be a real number. Prove that ...
 3.14: Find the point on the graph of (see figure) where the tangent line ...
 3.15: (a) Let be a positive number. Use the table feature of a graphing u...
 3.16: (a) Let be a positive number. Use the table feature of a graphing u...
 3.17: The police department must determine the speed limit on a bridge su...
 3.18: A legalsized sheet of paper (8.5 inches by 14 inches) is folded so...
 3.19: The polynomial is the quadratic approximation of the function at if...
Solutions for Chapter 3: Applications of Differentiation
Full solutions for Calculus  8th Edition
ISBN: 9780618502981
Solutions for Chapter 3: Applications of Differentiation
Get Full SolutionsChapter 3: Applications of Differentiation includes 107 full stepbystep solutions. This textbook survival guide was created for the textbook: Calculus, edition: 8. Since 107 problems in chapter 3: Applications of Differentiation have been answered, more than 78323 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Calculus was written by and is associated to the ISBN: 9780618502981.

Absolute value of a complex number
The absolute value of the complex number z = a + b is given by ?a2+b2; also, the length of the segment from the origin to z in the complex plane.

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

Center
The central point in a circle, ellipse, hyperbola, or sphere

Differentiable at x = a
ƒ'(a) exists

Directed distance
See Polar coordinates.

Directed line segment
See Arrow.

Distance (in a coordinate plane)
The distance d(P, Q) between P(x, y) and Q(x, y) d(P, Q) = 2(x 1  x 2)2 + (y1  y2)2

Distance (in Cartesian space)
The distance d(P, Q) between and P(x, y, z) and Q(x, y, z) or d(P, Q) ((x )  x 2)2 + (y1  y2)2 + (z 1  z 2)2

Focal length of a parabola
The directed distance from the vertex to the focus.

Histogram
A graph that visually represents the information in a frequency table using rectangular areas proportional to the frequencies.

Interquartile range
The difference between the third quartile and the first quartile.

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

Law of cosines
a2 = b2 + c2  2bc cos A, b2 = a2 + c2  2ac cos B, c2 = a2 + b2  2ab cos C

Right triangle
A triangle with a 90° angle.

Terms of a sequence
The range elements of a sequence.

Window dimensions
The restrictions on x and y that specify a viewing window. See Viewing window.

Wrapping function
The function that associates points on the unit circle with points on the real number line

yintercept
A point that lies on both the graph and the yaxis.

Zero factorial
See n factorial.

Zoom out
A procedure of a graphing utility used to view more of the coordinate plane (used, for example, to find theend behavior of a function).