Question

find and simplify the difference quotient $\frac{f(x + h)-f(x)}{h}$, $h
eq0$ for the given function.
f(x)= - 8
$\frac{f(x + h)-f(x)}{h}=$ (simplify your answer.)

Explanation:

Step1: Find f(x + h)

Since f(x)= - 8 is a constant function, f(x + h)= - 8.

Step2: Substitute into difference - quotient formula

Substitute f(x + h)= - 8 and f(x)= - 8 into $\frac{f(x + h)-f(x)}{h}$. We get $\frac{-8-(-8)}{h}$.

Step3: Simplify the numerator

$-8-(-8)=-8 + 8=0$, so the expression becomes $\frac{0}{h}$.

Step4: Simplify the fraction

$\frac{0}{h}=0$ for $h
eq0$.

Answer:

0