find the difference quotient $\frac{f(x + h)-f(x)}{h}$, where $h\neq0$, for the function below.\n\n$f(x)=-2x^…

find the difference quotient $\frac{f(x + h)-f(x)}{h}$, where $h\neq0$, for the function below.\n\n$f(x)=-2x^{2}+x$\n\nsimplify your answer as much as possible.\n\n$\frac{f(x + h)-f(x)}{h}=square$

find the difference quotient $\frac{f(x + h)-f(x)}{h}$, where $h\neq0$, for the function below.\n\n$f(x)=-2x^{2}+x$\n\nsimplify your answer as much as possible.\n\n$\frac{f(x + h)-f(x)}{h}=square$

Answer

Explanation:

Step1: Find $f(x + h)$

Substitute $x+h$ into $f(x)=-2x^{2}+x$. $f(x + h)=-2(x + h)^{2}+(x + h)=-2(x^{2}+2xh+h^{2})+x + h=-2x^{2}-4xh-2h^{2}+x + h$

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

$f(x + h)-f(x)=(-2x^{2}-4xh-2h^{2}+x + h)-(-2x^{2}+x)$ $=-2x^{2}-4xh-2h^{2}+x + h + 2x^{2}-x=-4xh-2h^{2}+h$

Step3: Calculate the difference - quotient

$\frac{f(x + h)-f(x)}{h}=\frac{-4xh-2h^{2}+h}{h}$ Factor out $h$ from the numerator: $\frac{h(-4x - 2h+1)}{h}$ Cancel out $h$ (since $h\neq0$), we get $-4x-2h + 1$

Answer:

$-4x-2h + 1$