Answer
The difference quotient for the provided function is $2x+h$.
Work Step by Step
Consider the provided function: $f\left( x \right)={{x}^{2}}$.
Now, substitute $x=x+h$ in the above equation to find $f\left( x+h \right)$
That is,
$f\left( x+h \right)={{\left( x+h \right)}^{2}}$
Now, apply the difference quotient formula,
$\begin{align}
& \frac{f\left( x+h \right)-f\left( x \right)}{h}=\frac{{{\left( x+h \right)}^{2}}-{{x}^{2}}}{h} \\
& =\frac{{{x}^{2}}+2xh+{{h}^{2}}-{{x}^{2}}}{h} \\
& =\frac{2xh+{{h}^{2}}}{h} \\
& =2x+h
\end{align}$
Hence, the difference quotient for the provided function is $2x+h$.
