Explanation Given data: y The derivative of function f is f ′ ( x ) = 3 e 2 x + 1 and f ( 0 ) = 2 Method/Formula used: The function f ( x ) is given by f ( x ) = ∫ ( f ′ ( x ) ) d x + A , where A is constant of integration determined by the given initial condition. The integration formula is ∫ e a x d x = 1 a e a x + A . Calculation: The derivative of the function f ( x ) is f ′ ( x ) = 3 e 2 x + 1 with f ( 0 ) = 2 . Therefore, f ( x ) = ∫ f ′ ( x ) d x = ∫ 3 e 2 x + 1 d x + A , where A is constant of integration

5th Edition

ISBN: 9781429241861

Author: Laura Taalman, Peter Kohn

Publisher: W. H. Freeman

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Chapter 4.4, Problem 3TF

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To find: The function f has given derivative f′ and value f(c) .

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Chapter 4.4, Problem 2TF

Chapter 4.4, Problem 4TF

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Chapter 4 Solutions

Calculus

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The function f has given derivative f ′ and value f ( c ) .

Solution Summary: The author calculates the derivative of the function f(x), where A is constant of integration determined by the initial condition.

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To find: The function f has given derivative f′ and value f(c) .

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Chapter 4 Solutions