given the following function, determine the difference quotient, $\frac{f(x + h)-f(x)}{h}$. $f(x)=-7x - 2$…
given the following function, determine the difference quotient, $\frac{f(x + h)-f(x)}{h}$. $f(x)=-7x - 2$ answer
Answer
Explanation:
Step1: Find f(x + h)
Substitute x + h into f(x): $f(x + h)=-7(x + h)-2=-7x-7h - 2$
Step2: Calculate f(x + h) - f(x)
$f(x + h)-f(x)=(-7x-7h - 2)-(-7x - 2)$ $=-7x-7h - 2 + 7x+2=-7h$
Step3: Calculate the difference quotient
$\frac{f(x + h)-f(x)}{h}=\frac{-7h}{h}=-7$
Answer:
$-7$