find the difference quotient (f(x + h)-f(x))/h, where h≠0, for the function below. f(x)=2x² - 6x + 2…

find the difference quotient (f(x + h)-f(x))/h, where h≠0, for the function below. f(x)=2x² - 6x + 2 simplify your answer as much as possible. (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)=2x² - 6x + 2 simplify your answer as much as possible. (f(x + h)-f(x))/h =

Answer

Explanation:

Step1: Find (f(x + h))

Substitute (x+h) into (f(x)): [ \begin{align*} f(x + h)&=2(x + h)^2-6(x + h)+2\ &=2(x^{2}+2xh+h^{2})-6x-6h + 2\ &=2x^{2}+4xh+2h^{2}-6x-6h + 2 \end{align*} ]

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

[ \begin{align*} f(x + h)-f(x)&=(2x^{2}+4xh+2h^{2}-6x-6h + 2)-(2x^{2}-6x + 2)\ &=2x^{2}+4xh+2h^{2}-6x-6h + 2-2x^{2}+6x - 2\ &=4xh+2h^{2}-6h \end{align*} ]

Step3: Find the difference - quotient

[ \begin{align*} \frac{f(x + h)-f(x)}{h}&=\frac{4xh+2h^{2}-6h}{h}\ &=\frac{h(4x + 2h-6)}{h}\ &=4x+2h - 6 \end{align*} ]

Answer:

(4x + 2h-6)