find the difference quotient (f(x + h)-f(x))/h, where h≠0, for the function below. f(x)=-3x² + 5x simplify…

find the difference quotient (f(x + h)-f(x))/h, where h≠0, for the function below. f(x)=-3x² + 5x 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)=-3x² + 5x 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)&=-3(x + h)^2+5(x + h)\ &=-3(x^{2}+2xh+h^{2})+5x + 5h\ &=-3x^{2}-6xh-3h^{2}+5x + 5h \end{align*} ]

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

[ \begin{align*} f(x + h)-f(x)&=(-3x^{2}-6xh-3h^{2}+5x + 5h)-(-3x^{2}+5x)\ &=-3x^{2}-6xh-3h^{2}+5x + 5h + 3x^{2}-5x\ &=-6xh-3h^{2}+5h \end{align*} ]

Step3: Find the difference - quotient

[ \begin{align*} \frac{f(x + h)-f(x)}{h}&=\frac{-6xh-3h^{2}+5h}{h}\ &=\frac{h(-6x - 3h+5)}{h}\ &=-6x-3h + 5 \end{align*} ]

Answer:

(-6x-3h + 5)