Question

given the following function, determine the difference quotient, $\frac{f(x + h)-f(x)}{h}$. $f(x)=-8x - 8$ answer 2 points

Explanation:

Step1: Find $f(x + h)$

Substitute $x+h$ into $f(x)$: $f(x + h)=-8(x + h)-8=-8x-8h - 8$

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

$f(x + h)-f(x)=(-8x-8h - 8)-(-8x - 8)=-8x-8h - 8 + 8x+8=-8h$

Step3: Compute the difference quotient

$\frac{f(x + h)-f(x)}{h}=\frac{-8h}{h}=-8$

Answer:

$-8$