Explanation Given: The function is f ( x ) = ( x + 3 ) 4 . Calculation: Evaluate f ′ ( x ) as follows. f ′ ( x ) = d d x ( ( x + 3 ) 4 ) = 4 ( x + 3 ) 3 Thus, f ′ ( x ) = 4 ( x + 3 ) 3 . Equate f ′ ( x ) to 0 to find the critical number. 4 ( x + 3 ) 3 = 0 x + 3 = 0 x = − 3 The critical numbers is x = − 3 . The second derivative f ″ ( x ) can be obtained from f ′ ( x ) = 4 ( x + 3 ) 3 as follows. f ″ ( x ) = d d x ( 4 ( x + 3 ) 3 ) = 4 ( 3 ( x + 3 ) 2 ) = 12 ( x + 3 ) 2 Thus, the value of f ″ ( x ) is f ″ ( x ) = 12 ( x + 3 ) 2 . Substitute x = − 3 in f ″ ( x ) = 12 ( x + 3 ) 2 . f ″ ( − 3 ) = 12 ( − 3 + 3 ) 2 = 0 Since, f ″ ( 0 ) = 0 , second derivative test fails

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Chapter 13.3, Problem 63E

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To find: The critical numbers for the given function and corresponding relative maxima or minima using the suitable derivative test.

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Chapter 13.3, Problem 62E

Chapter 13.3, Problem 64E

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Ch. 13.1 - Find where the function is increasing and...Ch. 13.1 - Prob. 2YT Ch. 13.1 - Prob. 3YT Ch. 13.1 - Prob. 4YT Ch. 13.1 - Prob. 1WE Ch. 13.1 - Prob. 2WE Ch. 13.1 - Prob. 3WE Ch. 13.1 - Prob. 4WE Ch. 13.1 - Prob. 5WE Ch. 13.1 - Prob. 6WE

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The critical numbers for the given function and corresponding relative maxima or minima using the suitable derivative test.

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To find: The critical numbers for the given function and corresponding relative maxima or minima using the suitable derivative test.

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