Explanation Given: The function is f ( x ) = x 3 + 3 x 2 − 3 . Formula Used: If f function, then a number c for which f ( c ) is defined and e i t h e r f ' ( 0 ) = 0 . The function f is said to have a local extremum at c if it has a local maximum or minimum there. If f has local extremum at x = c , then c is a critical number of f . Calculation: Consider the provided function: f ( x ) = x 3 + 3 x 2 − 3 Differentiate the function with respect to x . f ′ ( x ) = 3 x 2 + 3 ( 2 x ) = 3 x 2 + 6 x Solve for f ′ ( x ) = 0 to find the critical points. 3 x 2 + 6 x = 0 3 x ( x + 2 ) = 0 Further solve. 3 x = 0 x = 0 Or, x + 2 = 0 x = − 2 Use the first derivative test. Take points as x = − 2.5 , x = − 0

Mathematics with Applications, Books a la Carte, and MyLab Math with Pearson eText - Title-Specific Access Card Package (12th Edition)

12th Edition

ISBN: 9780134862651

Author: Lial

Publisher: PEARSON

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Chapter 12.1, Problem 19E

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To calculate: the location of local extremum of given function, f(x)=x3+3x2−3.

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Chapter 12.1, Problem 14E

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Chapter 12 Solutions

Mathematics with Applications, Books a la Carte, and MyLab Math with Pearson eText - Title-Specific Access Card Package (12th Edition)

Ch. 12.1 - Checkpoint 1 For what values of x is the function...Ch. 12.1 - Checkpoint 2 Find all intervals on which is...Ch. 12.1 - Checkpoint 3 Identity the x-values of all points...Ch. 12.1 - Checkpoint 4 Find the critical numbers for each of...Ch. 12.1 - Prob. 5CP Ch. 12.1 - Prob. 6CP Ch. 12.1 - Checkpoint 7 Find the locations of the local...Ch. 12.1 - Prob. 8CP Ch. 12.1 - Checkpoint 9 If a sales function is given by...Ch. 12.1 - Prob. 1E

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the location of local extremum of given function, f ( x ) = x 3 + 3 x 2 − 3 .

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