watch the video and then solve the problem given below. click here to watch the video. find the difference…

watch the video and then solve the problem given below. click here to watch the video. find the difference quotient of f; that is, find $\frac{f(x + h)-f(x)}{h}$, $h\neq0$, for the following function. be sure to simplify. $f(x)=2x^{2}-x - 1$ $\frac{f(x + h)-f(x)}{h}=square$ (simplify your answer.)

watch the video and then solve the problem given below. click here to watch the video. find the difference quotient of f; that is, find $\frac{f(x + h)-f(x)}{h}$, $h\neq0$, for the following function. be sure to simplify. $f(x)=2x^{2}-x - 1$ $\frac{f(x + h)-f(x)}{h}=square$ (simplify your answer.)

Answer

Explanation:

Step1: Find f(x + h)

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

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

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

Step3: Find the difference - quotient

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

Answer:

(4x + 2h-1)