Question

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

Explanation:

Step1: Find f(x + h)

Given f(x)=8x, then f(x + h)=8(x + h)=8x+8h.

Step2: Substitute into difference - quotient formula

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

Step3: Simplify the numerator

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

Step4: Cancel out h

Since $h
eq0$, $\frac{8h}{h}=8$.

Answer:

8