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# 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

Solutions for Chapter 3.2
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##### ISBN: 9780618502981

This expansive textbook survival guide covers the following chapters and their solutions. Chapter 3.2: Rolles Theorem and the Mean Value Theorem includes 85 full step-by-step 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 step-by-step 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.

Key Calculus Terms and definitions covered in this textbook
• 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.

• First-degree 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 + ae-kx, where a, b, c, and k are positive with b < 1. c is the limit to growth

• Negative linear correlation

See Linear correlation.

• Piecewise-defined 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>.

• y-intercept

A point that lies on both the graph and the y-axis.

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