find the difference quotient (f(x + h)-f(x))/h, where h≠0, for the function below. f(x)=2x² - 4 simplify…

find the difference quotient (f(x + h)-f(x))/h, where h≠0, for the function below. f(x)=2x² - 4 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 - 4 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)): [f(x + h)=2(x + h)^{2}-4=2(x^{2}+2xh+h^{2})-4=2x^{2}+4xh + 2h^{2}-4]

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

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

Step3: Calculate the difference - quotient

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

Answer:

(4x + 2h)