 3.2.1: In Exercises 14, explain why Rolles Theorem does not apply to the f...
 3.2.2: In Exercises 14, explain why Rolles Theorem does not apply to the f...
 3.2.3: In Exercises 14, explain why Rolles Theorem does not apply to the f...
 3.2.4: In Exercises 14, explain why Rolles Theorem does not apply to the f...
 3.2.5: In Exercises 58, find the two intercepts of the function and show ...
 3.2.6: In Exercises 58, find the two intercepts of the function and show ...
 3.2.7: In Exercises 58, find the two intercepts of the function and show ...
 3.2.8: In Exercises 58, find the two intercepts of the function and show ...
 3.2.9: Rolles Theorem In Exercises 9 and 10, the graph of is shown. Apply ...
 3.2.10: Rolles Theorem In Exercises 9 and 10, the graph of is shown. Apply ...
 3.2.11: In Exercises 1124, determine whether Rolles Theorem can be applied ...
 3.2.12: In Exercises 1124, determine whether Rolles Theorem can be applied ...
 3.2.13: In Exercises 1124, determine whether Rolles Theorem can be applied ...
 3.2.14: In Exercises 1124, determine whether Rolles Theorem can be applied ...
 3.2.15: In Exercises 1124, determine whether Rolles Theorem can be applied ...
 3.2.16: In Exercises 1124, determine whether Rolles Theorem can be applied ...
 3.2.17: In Exercises 1124, determine whether Rolles Theorem can be applied ...
 3.2.18: In Exercises 1124, determine whether Rolles Theorem can be applied ...
 3.2.19: In Exercises 1124, determine whether Rolles Theorem can be applied ...
 3.2.20: In Exercises 1124, determine whether Rolles Theorem can be applied ...
 3.2.21: In Exercises 1124, determine whether Rolles Theorem can be applied ...
 3.2.22: In Exercises 1124, determine whether Rolles Theorem can be applied ...
 3.2.23: In Exercises 1124, determine whether Rolles Theorem can be applied ...
 3.2.24: In Exercises 1124, determine whether Rolles Theorem can be applied ...
 3.2.25: In Exercises 2528, use a graphing utility to graph the function on ...
 3.2.26: In Exercises 2528, use a graphing utility to graph the function on ...
 3.2.27: In Exercises 2528, use a graphing utility to graph the function on ...
 3.2.28: In Exercises 2528, use a graphing utility to graph the function on ...
 3.2.29: Vertical Motion The height of a ball seconds after it is thrown upw...
 3.2.30: Reorder Costs The ordering and transportation cost for components u...
 3.2.31: In Exercises 31 and 32, copy the graph and sketch the secant line t...
 3.2.32: In Exercises 31 and 32, copy the graph and sketch the secant line t...
 3.2.33: Writing In Exercises 3336, explain why the Mean Value Theorem does ...
 3.2.34: Writing In Exercises 3336, explain why the Mean Value Theorem does ...
 3.2.35: Writing In Exercises 3336, explain why the Mean Value Theorem does ...
 3.2.36: Writing In Exercises 3336, explain why the Mean Value Theorem does ...
 3.2.37: Mean Value Theorem Consider the graph of the function (a) Find the ...
 3.2.38: Mean Value Theorem Consider the graph of the function (a) Find the ...
 3.2.39: In Exercises 39 46, determine whether the Mean Value Theorem can be...
 3.2.40: In Exercises 39 46, determine whether the Mean Value Theorem can be...
 3.2.41: In Exercises 39 46, determine whether the Mean Value Theorem can be...
 3.2.42: In Exercises 39 46, determine whether the Mean Value Theorem can be...
 3.2.43: In Exercises 39 46, determine whether the Mean Value Theorem can be...
 3.2.44: In Exercises 39 46, determine whether the Mean Value Theorem can be...
 3.2.45: In Exercises 39 46, determine whether the Mean Value Theorem can be...
 3.2.46: In Exercises 39 46, determine whether the Mean Value Theorem can be...
 3.2.47: In Exercises 47 50, use a graphing utility to (a) graph the functio...
 3.2.48: In Exercises 47 50, use a graphing utility to (a) graph the functio...
 3.2.49: In Exercises 47 50, use a graphing utility to (a) graph the functio...
 3.2.50: In Exercises 47 50, use a graphing utility to (a) graph the functio...
 3.2.51: Vertical Motion The height of an object seconds after it is dropped...
 3.2.52: Sales A company introduces a new product for which the number of un...
 3.2.53: Let be continuous on and differentiable on If there exists in such ...
 3.2.54: Let be continuous on the closed interval and differentiable on the ...
 3.2.55: The function is differentiable on and satisfies However, its deriva...
 3.2.56: Can you find a function such that f2 6, and for all Why or why not?...
 3.2.57: Speed A plane begins its takeoff at 2:00 P.M. on a 2500mile flight...
 3.2.58: Temperature When an object is removed from a furnace and placed in ...
 3.2.59: Velocity Two bicyclists begin a race at 8:00 A.M. They both finish ...
 3.2.60: Acceleration At 9:13 A.M., a sports car is traveling 35 miles per h...
 3.2.61: Graphical Reasoning The figure shows two parts of the graph of a co...
 3.2.62: Consider the function (a) Use a graphing utility to graph and (b) I...
 3.2.63: Think About It In Exercises 63 and 64, sketch the graph of an arbit...
 3.2.64: Think About It In Exercises 63 and 64, sketch the graph of an arbit...
 3.2.65: In Exercises 65 and 66, use the Intermediate Value Theorem and Roll...
 3.2.66: In Exercises 65 and 66, use the Intermediate Value Theorem and Roll...
 3.2.67: Determine the values and such that the function satisfies the hypot...
 3.2.68: Determine the values and so that the function satisfies the hypothe...
 3.2.69: Differential Equations In Exercises 6972, find a function that has ...
 3.2.70: Differential Equations In Exercises 6972, find a function that has ...
 3.2.71: Differential Equations In Exercises 6972, find a function that has ...
 3.2.72: Differential Equations In Exercises 6972, find a function that has ...
 3.2.73: True or False? In Exercises 7376, determine whether the statement i...
 3.2.74: True or False? In Exercises 7376, determine whether the statement i...
 3.2.75: True or False? In Exercises 7376, determine whether the statement i...
 3.2.76: True or False? In Exercises 7376, determine whether the statement i...
 3.2.77: Prove that if and is any positive integer, then the polynomial func...
 3.2.78: Prove that if for all in an interval then is constant on xy
 3.2.79: Let Prove that for any interval the value guaranteed by the Mean Va...
 3.2.80: (a) Let and Then and Show that there is at least one value in the i...
 3.2.81: Prove that if is differentiable on and for all real numbers, then h...
 3.2.82: Use the result of Exercise 81 to show that has at most one fixed po...
 3.2.83: Prove that for all and 10x21
 3.2.84: Prove that for all and x21y
 3.2.85: Let Use the Mean Value Theorem to show that 21y
Solutions for Chapter 3.2: Rolles Theorem and the Mean Value Theorem
Full solutions for Calculus  8th Edition
ISBN: 9780618502981
Solutions for Chapter 3.2: Rolles Theorem and the Mean Value Theorem
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Chapter 3.2: Rolles Theorem and the Mean Value Theorem includes 85 full stepbystep solutions. Since 85 problems in chapter 3.2: Rolles Theorem and the Mean Value Theorem have been answered, more than 24079 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Calculus, edition: 8. Calculus was written by Patricia and is associated to the ISBN: 9780618502981.

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

Blocking
A feature of some experimental designs that controls for potential differences between subject groups by applying treatments randomly within homogeneous blocks of subjects

Branches
The two separate curves that make up a hyperbola

Constraints
See Linear programming problem.

Descriptive statistics
The gathering and processing of numerical information

Differentiable at x = a
ƒ'(a) exists

Domain of a function
The set of all input values for a function

Equation
A statement of equality between two expressions.

Factored form
The left side of u(v + w) = uv + uw.

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

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)

Logistic growth function
A model of population growth: ƒ1x2 = c 1 + a # bx or ƒ1x2 = c1 + aekx, where a, b, c, and k are positive with b < 1. c is the limit to growth

Negative linear correlation
See Linear correlation.

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

Positive angle
Angle generated by a counterclockwise rotation.

Power rule of logarithms
logb Rc = c logb R, R 7 0.

Secant line of ƒ
A line joining two points of the graph of ƒ.

Solve algebraically
Use an algebraic method, including paper and pencil manipulation and obvious mental work, with no calculator or grapher use. When appropriate, the final exact solution may be approximated by a calculator

Vector equation for a line in space
The line through P0(x 0, y0, z0) in the direction of the nonzero vector V = <a, b, c> has vector equation r = r0 + tv , where r = <x,y,z>.

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