Explanation Calculation: The given function is, f ( x ) = x 3 − 3 x 2 − 24 x + 5 . Differentiate the above function with respect to x . f x ( x ) = d d x ( x 3 − 3 x 2 − 24 x + 5 ) = d d x ( x 3 ) − 3 d d x ( x 2 ) − 24 d d x ( x ) + d d x ( 5 ) = 3 x 2 − 3 ( 2 x ) − 24 = 3 x 2 − 6 x − 24 Calculate the second derivative of the function f ( x ) by differentiate the function f x with respect to x . f x x ( x ) = d d x ( f x ( x , y ) ) = d d x ( 3 x 2 − 6 x − 24 ) = d d x ( 3 x 2 ) − d d x ( 6 x ) − d d x ( 24 ) = 6 x − 6 That is, f x x ( x ) = 6 x − 6 (1) Obtain the critical points of the function by equate the function f x ( x ) = 0 . 3 x 2 − 6 x − 24 = 0 x 2 − 2 x − 8 = 0 ( x − 4 ) ( x + 2 ) = 0 x = 4 or x = − 2 Therefore, the critical point of the function are x = 4 and x = − 2 . Calculate the second derivative of the function f ( x ) at the point x = 4 . Substitute the value x = 4 in the function f x x ( x ) = 6 x − 6

Finite Mathematics and Calculus with Applications (10th Edition)

10th Edition

ISBN: 9780321979407

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter 17.3, Problem 1WE

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To find: The set of all extrema of the function f(x)=x3−3x2−24x+5 .

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The set of all extrema of the function f ( x ) = x 3 − 3 x 2 − 24 x + 5 .

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To find: The set of all extrema of the function f(x)=x3−3x2−24x+5 .

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Chapter 17 Solutions