Question

find and simplify the difference quotient $\frac{f(x + h)-f(x)}{h}$, $h
eq0$ for the given function. f(x)= - 4 $\frac{f(x + h)-f(x)}{h}=square$ (simplify your answer.)

Explanation:

Step1: Find f(x + h)

Since f(x)= - 4 is a constant - function, f(x + h)= - 4.

Step2: Substitute into the difference - quotient formula

Substitute f(x + h)= - 4 and f(x)= - 4 into $\frac{f(x + h)-f(x)}{h}$. We get $\frac{-4-(-4)}{h}$.

Step3: Simplify the numerator

-4-(-4)=-4 + 4 = 0. So the expression becomes $\frac{0}{h}$.

Step4: Simplify the fraction

$\frac{0}{h}=0$ for h≠0.

Answer:

0