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Find f'(t) if f(t)=4t² +8t+3.

Find f'(t) if f(t)=4t² +8t+3.

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:** Find \( f'(t) \) if \( f(t) = 4t^2 + 8t + 3 \). **Solution:** To find the derivative \( f'(t) \), apply the power rule to each term in the function \( f(t) = 4t^2 + 8t + 3 \). - The derivative of \( 4t^2 \) is \( 8t \) (using the power rule: \((at^n)' = nat^{n-1}\)). - The derivative of \( 8t \) is \( 8 \) (since \((at)' = a\)). - The derivative of the constant \( 3 \) is \( 0 \). Thus, the derivative \( f'(t) = 8t + 8 \). **Answer:** \( f'(t) = 8t + 8 \)
Transcribed Image Text:**Question:** Find \( f'(t) \) if \( f(t) = 4t^2 + 8t + 3 \). **Solution:** To find the derivative \( f'(t) \), apply the power rule to each term in the function \( f(t) = 4t^2 + 8t + 3 \). - The derivative of \( 4t^2 \) is \( 8t \) (using the power rule: \((at^n)' = nat^{n-1}\)). - The derivative of \( 8t \) is \( 8 \) (since \((at)' = a\)). - The derivative of the constant \( 3 \) is \( 0 \). Thus, the derivative \( f'(t) = 8t + 8 \). **Answer:** \( f'(t) = 8t + 8 \)
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