Explanation Given Data: Write the given function as follows. f ( x ) = ( x − 5 ) 2 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 ) = ( x − 5 ) 2 as follows. f ( x ) = x 2 + 5 2 − 10 x f ( x ) = x 2 − 10 x 1 + 25 x 0 (1) From the antiderivative function formula, the antiderivative function for the function in equation (1) is written as follows. F ( x ) = x 2 + 1 2 + 1 − 10 ( x 1 + 1 1 + 1 ) + 25 ( x 0 + 1 0 + 1 ) + C = x 3 3 − 10 ( x 2 2 ) + 25 x + C = 1 3 x 3 − 5 x 2 + 25 x + C Thus, the most general antiderivative of the function f ( x ) = ( x − 5 ) 2 is 1 3 x 3 − 5 x 2 + 25 x + C _

Single Variable Calculus: Early Transcendentals, Volume I

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ISBN: 9781305270343

Author: James Stewart

Publisher: Cengage Learning

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Chapter 4.9, Problem 6E

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To find: The most general antiderivative of the function f(x)=(x−5)2 and check the determined antiderivative for the function f(x)=(x−5)2 by differentiation.

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Chapter 4.9, Problem 5E

Chapter 4.9, Problem 7E

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Single Variable Calculus: Early Transcendentals, Volume I

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The most general antiderivative of the function f ( x ) = ( x − 5 ) 2 and check the determined antiderivative for the function f ( x ) = ( x − 5 ) 2 by differentiation.

Solution Summary: The author explains how to find the most general antiderivative of the function f(x)= left (x-5 )2 by differentiation.

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To find: The most general antiderivative of the function f(x)=(x−5)2 and check the determined antiderivative for the function f(x)=(x−5)2 by differentiation.

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Chapter 4 Solutions