Explanation The first derivative test for relative extrema consists of following steps: Find all the critical points of a continuous function defined on an interval ( a , b ) . Let’s say ‘c’. If f ' ( x ) changes sign from positive to negative as x increases through c, then c is a point of local maxima, and f ( c ) is local maximum value. If f ' ( x ) changes sign from negative to positive as x increases through c, then c is a point of local minima, and f f ( c ) is local minimum value. If f ' ( x ) does not change sign as x increases through c, then c is neither a point of local minima nor a point of local maxima. Such a point is called a point of inflection. Given, f ( x ) = ( x 3 − 3 x + 1 ) 7 Now differentiating with respect to ‘x’

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Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

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Chapter 4.3, Problem 34PS

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Relative maxima and relative minima using first derivative test.

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Relative maxima and relative minima using first derivative test.

Solution Summary: The author explains how the first derivative test for relative extrema consists of finding all the critical points of a continuous function defined on an interval.

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