Question

given the following function, determine the difference quotient, $\frac{f(x + h)-f(x)}{h}$. $f(x)=-7x - 4$

Explanation:

Step1: Find f(x + h)

Substitute x + h into f(x):
$f(x + h)=-7(x + h)-4=-7x-7h - 4$

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

$f(x + h)-f(x)=(-7x-7h - 4)-(-7x - 4)$
$=-7x-7h - 4 + 7x + 4=-7h$

Step3: Calculate the difference quotient

$\frac{f(x + h)-f(x)}{h}=\frac{-7h}{h}=-7$

Answer:

$-7$