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If ƒ(x) = (x² + 4x + 5)², then f'(x) = 4x³ + 24x² +52x + 40 f'(2) =

If ƒ(x) = (x² + 4x + 5)², then f'(x) = 4x³ + 24x² +52x + 40 f'(2) =

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
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.
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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