find the difference quotient of f, that is, find (f(x + h)-f(x))/h, h≠0, for the following function. be sure…

Explanation:

Step1: Find f(x + h)

Substitute (x+h) into (f(x)): [f(x + h)=(x + h)^2-9(x + h)+9=x^{2}+2xh+h^{2}-9x-9h + 9]

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

[ \begin{align*} f(x + h)-f(x)&=(x^{2}+2xh+h^{2}-9x-9h + 9)-(x^{2}-9x + 9)\ &=x^{2}+2xh+h^{2}-9x-9h + 9-x^{2}+9x - 9\ &=2xh+h^{2}-9h \end{align*} ]

Step3: Find the difference - quotient

[ \begin{align*} \frac{f(x + h)-f(x)}{h}&=\frac{2xh+h^{2}-9h}{h}\ &=\frac{h(2x + h-9)}{h}\ &=2x+h - 9 \end{align*} ]

Answer:

(2x+h - 9)