Find the difference quotient $$ \frac{f(x+h)-f(x)}{h} $$, where $$ h \neq 0 $$, for the function below. $$ f(x)=-3 x^{2}-x+2 $$ Simplify your answer as much as possible. $$ \frac{f(x+h)-f(x)}{h}= $$

Question

UpStudy AI · Accepted Answer

Calculate or simplify the expression $$ \frac{-3(x+h)^{2}-(x+h)+2-(-3x^{2}-x+2)}{h} $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\frac{-3\left(x+h\right)^{2}-\left(x+h\right)+2-\left(-3x^{2}-x+2\right)}{h}$$
- step1: Remove the parentheses:
  $$\frac{-3\left(x+h\right)^{2}-\left(x+h\right)+2+3x^{2}+x-2}{h}$$
- step2: Calculate:
  $$\frac{-6xh-3h^{2}-h}{h}$$
- step3: Rewrite the fraction:
  $$-\frac{6xh+3h^{2}+h}{h}$$
- step4: Factor:
  $$-\frac{h\left(6x+3h+1\right)}{h}$$
- step5: Reduce the fraction:
  $$-\left(6x+3h+1\right)$$
- step6: Calculate:
  $$-6x-3h-1$$
The difference quotient $$ \frac{f(x+h)-f(x)}{h} $$ for the function $$ f(x)=-3x^{2}-x+2 $$ is $$ -6x-3h-1 $$.
The difference quotient is $$ -6x - 3h - 1 $$.

Find the difference quotient , where , for the function below.

Simplify your answer as much as possible.

Solución de inteligencia artificial de Upstudy

Responder

Solución

The Deep Dive

preguntas relacionadas

Latest Calculus Questions

Find the difference quotient , where , for the function below. Simplify your answer as much as possible.