Answer
The difference quotient for the given function is $2x+h$
Work Step by Step
$f(x)=x^{2}$
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:
$f(x+h)=(x+h)^{2}=x^{2}+2xh+h^{2}$
Substitute the known values into the formula for the difference quotient:
$\dfrac{f(x+h)-f(x)}{h}=\dfrac{x^{2}+2xh+h^{2}-x^{2}}{h}=\dfrac{2xh+h^{2}}{h}=...$
Take out common factor $h$ from the numerator and simplify:
$...=\dfrac{h(2x+h)}{h}=2x+h$
The difference quotient for the given function is $2x+h$
