Precalculus (6th Edition) Blitzer

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

Chapter 4 - Section 4.2 - Trigonometric Functions: The Unit Circle - Exercise Set - Page 550: 105


The value of given expression is $6x+3h-1$.

Work Step by Step

Substitute the value of $f\left( x \right)=3{{x}^{2}}-x+5$ in the main expression: $\begin{align} & \frac{f\left( x+h \right)-f\left( x \right)}{h}=\frac{3{{\left( x+h \right)}^{2}}-\left( x+h \right)+5-\left( 3{{x}^{2}}-x+5 \right)}{h} \\ & =\frac{3\left( {{x}^{2}}+2xh+{{h}^{2}} \right)-x-h+5-3{{x}^{2}}+x-5}{h} \\ & =\frac{3{{x}^{2}}+6xh+3{{h}^{2}}-x-h+5-3{{x}^{2}}+x-5}{h} \\ & =6x+3h-1 \end{align}$ Thus, the value of given expression is $6x+3h-1$.
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