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)

$f(x + h)-f(x)=(x^{2}+2xh+h^{2}-9x - 9h + 9)-(x^{2}-9x + 9)$ $=x^{2}+2xh+h^{2}-9x - 9h + 9 - x^{2}+9x - 9=2xh+h^{2}-9h$

Step3: Find the difference - quotient

$\frac{f(x + h)-f(x)}{h}=\frac{2xh+h^{2}-9h}{h}$ Factor out h from the numerator: $\frac{h(2x + h-9)}{h}$ Cancel out h (since h≠0): $2x+h - 9$

Answer:

$2x+h - 9$