## Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning

# Chapter 2 - Section 2.8 - The Derivative as a Function - 2.8 Exercises: 21

#### Answer

$f'(x)=3$

#### Work Step by Step

$f(x)=3x-8$ Derivative of a function using the definition: $f'(x)=\lim\limits_{h \to 0}\dfrac{f(x+h)-f(x)}{h}$ To find $f(x+h)$, wherever you find $x$ in the function, substitute $x+h$ $f(x+h)=3(x+h)-8=3x+3h-8$ Let's plug in the components of the formula: $f'(x)=\dfrac{3x+3h-8-3x+8}{h}=\dfrac{3h}{h}=3$ $f'(x)=3$

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