Explanation Given Data: Write the given function as follows. f ( x ) = 3 x − 2 x 3 Formula used 1: The antiderivative function for the function x n is x n + 1 n + 1 + C . Here, C is the constant. Formula used 2: Write the required differentiation formula to verify the answer as follows. d d x ( x n ) = n x n − 1 d d x ( c o n s tan t ) = 0 Calculation: Rewrite the function f ( x ) = 3 x − 2 x 3 as follows. f ( x ) = 3 x 1 2 − 2 x 1 3 (1) From the antiderivative function formula, the antiderivative function for the function in equation (1) is written as follows. F ( x ) = 3 ( x 1 2 + 1 1 2 + 1 ) − 2 ( x 1 3 + 1 1 3 + 1 ) + C = 3 ( x 3 2 3 2 ) − 2 ( x 4 3 4 3 ) + C = 2 x 3 2 − 3 2 x 4 3 + C Thus, the most general antiderivative of the function f ( x ) = 3 x − 2 x 3 is 2 x 3 2 − 3 2 x 4 3 + C _ . Here the determined antiderivative for the function f ( x ) = 3 x − 2 x 3 is 2 x 3 2 − 3 2 x 4 3 + C

Essential Calculus: Early Transcendentals; MAC 2311 Sequence| MAC 2281Sequence USF (Essential Calculus)

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ISBN: 9781285101552

Author: James Stewart

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Chapter 4.7, Problem 5E

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To find: The most general antiderivative of the function f(x)=3x−2x3 and check determined antiderivative for the function f(x)=3x−2x3 by differentiation.

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Chapter 4.7, Problem 3E

Chapter 4.7, Problem 4E

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Essential Calculus: Early Transcendentals; MAC 2311 Sequence| MAC 2281Sequence USF (Essential Calculus)

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The most general antiderivative of the function f ( x ) = 3 x − 2 x 3 and check determined antiderivative for the function f ( x ) = 3 x − 2 x 3 by differentiation .

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To find: The most general antiderivative of the function f(x)=3x−2x3 and check determined antiderivative for the function f(x)=3x−2x3 by differentiation.

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Chapter 4 Solutions