#### Answer

The average rate of change of $f\left( x \right)=3x$ from ${{x}_{1}}=0\text{ to }{{x}_{2}}=5$ is $3$.

#### Work Step by Step

Consider the provided function $f\left( x \right)=3x$.
The value of function $f\left( x \right)=3x$ at ${{x}_{1}}=0$ is:
$\begin{align}
& f\left( 0 \right)=3\left( 0 \right) \\
& =0
\end{align}$
The value of function $f\left( x \right)=3x$ at ${{x}_{2}}=5$ is:
$\begin{align}
& f\left( 5 \right)=3\left( 5 \right) \\
& =15
\end{align}$
The average rate of change of $f$ from ${{x}_{1}}=0\text{ to }{{x}_{2}}=5$ is:
$\begin{align}
& \frac{\Delta y}{\Delta x}=\frac{f\left( 5 \right)-f\left( 0 \right)}{5-0} \\
& =\frac{15-0}{5-0} \\
& =\frac{15}{5} \\
& =3
\end{align}$
Thus, the average rate of change of $f\left( x \right)=3x$ from ${{x}_{1}}=0\text{ to }{{x}_{2}}=5$ is $3$.