Answer
The difference quotient for the given function is $4$
Work Step by Step
$f(x)=4x$
Find the difference quotient $\dfrac{f(x+h)-f(x)}{h}$
Start by finding $f(x+h)$. Substitute $x$ by $x+h$ in $f(x)$ and simplify:
$f(x+h)=4(x+h)=4x+4h$
Substitute the known values into the formula for the difference quotient and simplify:
$\dfrac{f(x+h)-f(x)}{h}=\dfrac{4x+4h-4x}{h}=\dfrac{4h}{h}=4$
The difference quotient for the given function is $4$
