find the difference quotient f(x + h)-f(x)/h, where h≠0, for the function below. f(x)=4x² - x + 7 simplify…

find the difference quotient f(x + h)-f(x)/h, where h≠0, for the function below. f(x)=4x² - x + 7 simplify your answer as much as possible. answer submitted: f(x + h)-f(x)/h =

find the difference quotient f(x + h)-f(x)/h, where h≠0, for the function below. f(x)=4x² - x + 7 simplify your answer as much as possible. answer submitted: f(x + h)-f(x)/h =

Answer

Explanation:

Step1: Find $f(x + h)$

Substitute $x+h$ into $f(x)$: [ \begin{align*} f(x + h)&=4(x + h)^2-(x + h)+7\ &=4(x^{2}+2xh+h^{2})-x - h+7\ &=4x^{2}+8xh+4h^{2}-x - h+7 \end{align*} ]

Step2: Calculate $f(x + h)-f(x)$

[ \begin{align*} f(x + h)-f(x)&=(4x^{2}+8xh+4h^{2}-x - h+7)-(4x^{2}-x + 7)\ &=4x^{2}+8xh+4h^{2}-x - h+7 - 4x^{2}+x - 7\ &=8xh+4h^{2}-h \end{align*} ]

Step3: Find the difference - quotient

[ \begin{align*} \frac{f(x + h)-f(x)}{h}&=\frac{8xh+4h^{2}-h}{h}\ &=\frac{h(8x + 4h-1)}{h}\ &=8x + 4h-1 \end{align*} ]

Answer:

$8x + 4h-1$