Explanation Theorem used: First derivative Test: Assume f is continuous on an interval that contains a critical point c and assume f is differentiable on an interval containing c , except perhaps at c itself. If f ′ changes sign from positive to negative as x increase through c , then f has a local maximum at c . If f ′ changes sign from negative to positive as x increase through c , then f has a local minima at c . If f ′ positive on both sides near c or negative on both sides near c , then f has no local extreme value at c. Calculation: Consider the function f ( x ) = x 2 . Differentiate with respect to x on both sides, d d x ( f ( x ) ) = d

Calculus, Single Variable: Early Transcendentals (3rd Edition)

3rd Edition

ISBN: 9780134766850

Author: William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher: PEARSON

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Chapter 4.3, Problem 3QC

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To explain: The first derivative test whether f(x)=x2 has a local maxima or local minima at the critical point x=0.

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Chapter 4.3, Problem 2QC

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Chapter 4 Solutions

Calculus, Single Variable: Early Transcendentals (3rd Edition)

Ch. 4.1 - Sketch the graph of a function that is continuous...Ch. 4.1 - Consider the function f(x) = x3. Where is the...Ch. 4.1 - Sketch the graph of a function that is continuous...Ch. 4.1 - Sketch the graph of a function that has an...Ch. 4.1 - What is a critical point of a function?Ch. 4.1 - Sketch the graph of a function f that has a local...Ch. 4.1 - Sketch the graph of a function f that has a local...Ch. 4.1 - Absolute maximum/minimum values Use the following...Ch. 4.1 - Prob. 12E Ch. 4.1 - Absolute maximum/minimum values Use the following...

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The first derivative test whether f ( x ) = x 2 has a local maxima or local minima at the critical point x = 0 .

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To explain: The first derivative test whether f(x)=x2 has a local maxima or local minima at the critical point x=0.

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Chapter 4 Solutions