Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 1 - Section 1.3 - More on Functions and Their Graphs - Exercise Set - Page 198: 76

Answer

The difference quotient for the provided function is $4x+2h$.

Work Step by Step

Consider the provided function: $f\left( x \right)=2{{x}^{2}}$. Now, substitute $x=x+h$ in the above equation to find $f\left( x+h \right)$ That is, $f\left( x+h \right)=2{{\left( x+h \right)}^{2}}$ Now, apply the difference quotient formula, $\begin{align} & \frac{f\left( x+h \right)-f\left( x \right)}{h}=\frac{2{{\left( x+h \right)}^{2}}-2{{x}^{2}}}{h} \\ & =\frac{2{{x}^{2}}+4xh+2{{h}^{2}}-2{{x}^{2}}}{h} \\ & =\frac{h\left( 4x+2h \right)}{h} \\ & =4x+2h \end{align}$ Hence, the difference quotient for the provided function is $4x+2h$.
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