Question

In Exercises 27–28, find and simplify the difference quotient f(x + h) - f(x) hFor the given function: f(x)=8x-11

Answer 1

$f(x)=8x-11$

find:

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

find f(x+h)

$\begin{gathered} f(x+h)=8(x+h)-11 \\ f(x+h)=8x+8h-11 \end{gathered}$

replace in the quotient

$\frac{(8x+8h-11)-(8x-11)}{h}$

simplify,

$\begin{gathered} \frac{8h}{h} \\ 8 \end{gathered}$

answer:

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