Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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If \( f(x) = \left( x^2 + 4x + 5 \right)^2 \), then \[ f'(x) = 4x^3 + 24x^2 + 52x + 40 \] \( f'(2) = \) Explanation: - The function \( f(x) \) is given as the square of the quadratic expression \( x^2 + 4x + 5 \). - The derivative \( f'(x) \) is a cubic polynomial \( 4x^3 + 24x^2 + 52x + 40 \). - The task involves evaluating the derivative at \( x = 2 \), given in the last part of the text where \( f'(2) \) is to be computed.
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Transcribed Image Text:If \( f(x) = \left( x^2 + 4x + 5 \right)^2 \), then \[ f'(x) = 4x^3 + 24x^2 + 52x + 40 \] \( f'(2) = \) Explanation: - The function \( f(x) \) is given as the square of the quadratic expression \( x^2 + 4x + 5 \). - The derivative \( f'(x) \) is a cubic polynomial \( 4x^3 + 24x^2 + 52x + 40 \). - The task involves evaluating the derivative at \( x = 2 \), given in the last part of the text where \( f'(2) \) is to be computed.
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