Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 1 - Functions - Review Exercises: 18

Answer

$\dfrac{f(x+h)-f(x)}{h}=-5$ $\dfrac{f(x)-f(a)}{x-a}=-5$

Work Step by Step

$f(x)=4-5x$ $\textbf{Evaluate}$ $\dfrac{f(x+h)-f(x)}{h}$ First, substitute $x$ by $x+h$ in the given function and simplify to find $f(x+h)$: $f(x+h)=4-5(x+h)=4-5x-5h$ Substitute $f(x+h)$ and $f(x)$ into the difference quotient formula and simplify: $\dfrac{f(x+h)-f(x)}{h}=\dfrac{4-5x-5h-(4-5x)}{h}=...$ $...=\dfrac{4-5x-5h-4+5x}{h}=\dfrac{-5h}{h}=-5$ $\textbf{Evaluate}$ $\dfrac{f(x)-f(a)}{x-a}$ Substitute $x$ by $a$ in $f(x)$ to find $f(a)$: $f(a)=4-5a$ Substitute $f(a)$ and $f(x)$ into the difference quotient formula and simplify: $\dfrac{f(x)-f(a)}{x-a}=\dfrac{4-5x-(4-5a)}{x-a}=\dfrac{4-5x-4+5a}{x-a}=...$ $...=\dfrac{-5x+5a}{x-a}=...$ Take out common factor $-5$ from the numerator and simplify again: $...=\dfrac{-5(x-a)}{x-a}=-5$
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