Explanation Given that, the second derivative is − 6 x . Integrate the second derivative as, f ′ ( x ) = ∫ − 6 x d x = − 6 ∫ x d x = − 6 [ x 2 2 ] + C 1 = − 3 x 2 + C 1 Since the slope is –3, for x = − 1 , substitute f ′ ( x ) = − 3 and x = − 1 in f ′ ( x ) = − 3 x 2 + C 1 . − 3 = − 3 ( − 1 ) 2 + C 1 − 3 = − 3 ( 1 ) + C 1 C 1 = 0 Thus, the first derivative is d y d x = − 3 x 2

Mylab Math With Pearson Etext -- 18 Week Standalone Access Card -- For Basic Technical Mathematics With Calculus

11th Edition

ISBN: 9780135902912

Author: Allyn J. Washington

Publisher: PEARSON

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Chapter 25, Problem 40RE

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The equation of the curve for which the second derivative is −6x and if the curve passes through (−1,3) with a slope of –3.

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Chapter 25, Problem 39RE

Chapter 25, Problem 41RE

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Chapter 25 Solutions

Mylab Math With Pearson Etext -- 18 Week Standalone Access Card -- For Basic Technical Mathematics With Calculus

Ch. 25.1 - Find an antiderivative of x3 + 4x. Ch. 25.1 - Prob. 2PE Ch. 25.1 - Prob. 1E Ch. 25.1 - Prob. 2E Ch. 25.1 - Prob. 3E Ch. 25.1 - Prob. 4E Ch. 25.1 - In Exercises 5–12, determine the value of a that...Ch. 25.1 - Prob. 6E Ch. 25.1 - Prob. 7E Ch. 25.1 - Prob. 8E

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The equation of the curve for which the second derivative is − 6 x and if the curve passes through ( − 1 , 3 ) with a slope of –3.

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The equation of the curve for which the second derivative is −6x and if the curve passes through (−1,3) with a slope of –3.

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Chapter 25 Solutions