Explanation Given information: f has a local maximum at x = c f has a local minimum at x = c f is continuous on [ a , b ] f is differentiable on ( a , b ) The secant line from ( a , f ( a ) ) to ( b , f ( b ) ) The right derivative f ' + ( c ) at a point x = c The left derivative f ' − ( c ) at a point x = c Extreme Value Theorem The Intermediate Value Theorem Calculation: f has a local maximum at x = c if there exists some δ > 0 such that f ( c ) ≥ f ( x ) ∀ x ∈ ( c − δ , c + δ ) f has a local minimum at x = c if there exists some δ > 0 such that f ( c ) ≤ f ( x ) ∀ x ∈ ( c − δ , c + δ ) f is said to be continuous on [ a , b ] if it is continuous at all points in the interval ( a , b ) and also right continuous at and right continuous at a and left continuous at b . f is said to be differentiable on ( a , b ) if it is continuous at all points in the interval ( a , b )

14th Edition

ISBN: 9781464140051

Author: TAALMAN, Laura, Kohn, Peter

Publisher: W. H. Freeman

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Chapter 3.1, Problem 1TB

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To state the given definitions and theorems.

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Chapter 2, Problem DCP

Chapter 3.1, Problem 0C

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Chapter 3 Solutions

Loose-leaf Version for Calculus

Ch. 3.1 - Prob. 1TB Ch. 3.1 - Prob. 0C Ch. 3.1 - Prob. 1C Ch. 3.1 - Prob. 2C Ch. 3.1 - Prob. 3C Ch. 3.1 - Prob. 4C Ch. 3.1 - Prob. 5C Ch. 3.1 - Prob. 6C Ch. 3.1 - Prob. 7C Ch. 3.1 - Prob. 8C

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ACP Ch. 3 - Prob. BCP Ch. 3 - Prob. CCP Ch. 3 - Prob. DCP

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To state the given definitions and theorems.

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