Explanation Given: The given function is h ( t ) = t 4 − 2 t 3 + 6 t 2 − 3 t + 10 . Formula used: The formula to calculate the differential of a function h ( x ) = [ g ( x ) ] n by General Power Rule is, h ′ ( x ) = n [ g ( x ) ] n − 1 g ′ ( x ) Calculation: The given function is, h ( t ) = t 4 − 2 t 3 + 6 t 2 − 3 t + 10 (1) Differentiate equation (1) with respect to t on both sides to evaluate h ′ ( t ) . h ′ ( t ) = d d t ( t 4 − 2 t 3 + 6 t 2 − 3 t + 10 ) = d d t ( t 4 ) − d d t ( 2 t 3 ) + d d t ( 6 t 2 ) − d d t ( 3 t ) + d d t ( 10 ) = 4 t 4 − 1 − 2 ⋅ 3 t 3 − 1 + 6 ⋅ 2 t 2 − 1 − 3 t 1 − 1 + 0 [ Use General Power Rule d d x ( x n ) = n x n − 1 , n > 0 ] h ′ ( t ) = 4 t 3 − 6 t 2 + 12 t − 3 [ ∵ t 0 = 1 ] Again differentiate above equation with respect to t on the both sides, to evaluate h ″ ( t )

Applied Calculus for the Managerial, Life, and Social Sciences

10th Edition

ISBN: 9781305887831

Author: Tan

Publisher: CENGAGE CO

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Chapter 3.5, Problem 5E

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To find: The second derivative of given function.

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Chapter 3.5, Problem 4E

Chapter 3.5, Problem 6E

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Chapter 3 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences

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The second derivative of given function.

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To find: The second derivative of given function.

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Chapter 3 Solutions