Find the difference quotient of $$ f $$, that is, find $$ \frac{f(x+h)-f(x)}{h}, h
eq 0 $$, for the following function $$ f(x)=x^{2}-6 x+7 $$ $$ \frac{f(x+h)-f(x)}{h}=\square $$ (Simplify your answer.)

Question

Find the difference quotient of $$ f $$, that is, find $$ \frac{f(x+h)-f(x)}{h}, h 
eq 0 $$, for the following function $$ f(x)=x^{2}-6 x+7 $$ $$ \frac{f(x+h)-f(x)}{h}=\square $$ (Simplify your answer.)

UpStudy AI · Accepted Answer

Calculate or simplify the expression $$ \frac{(x+h)^2-6(x+h)+7-x^2+6x-7}{h} $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\frac{\left(x+h\right)^{2}-6\left(x+h\right)+7-x^{2}+6x-7}{h}$$
- step1: Simplify:
  $$\frac{\left(x+h\right)^{2}-6\left(x+h\right)-x^{2}+6x}{h}$$
- step2: Calculate:
  $$\frac{2xh+h^{2}-6h}{h}$$
- step3: Factor:
  $$\frac{h\left(2x+h-6\right)}{h}$$
- step4: Reduce the fraction:
  $$2x+h-6$$
The difference quotient of the function $$ f(x) = x^{2} - 6x + 7 $$ is $$ 2x + h - 6 $$.
The difference quotient is $$ 2x + h - 6 $$.

Find the difference quotient of , that is, find , for the following function

(Simplify your answer.)

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Find the difference quotient of , that is, find , for the following function (Simplify your answer.)