Given, \(\displaystyle{f{{\left({x}\right)}}}={5}{x}\) from \(\displaystyle{x}_{{{1}}}={0}\) to \(\displaystyle{x}_{{{2}}}={3}\).

Step 3

Average rate of change is given by

\(A(x)=\frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1}}\)

\(\displaystyle={\frac{{{f{{\left({3}\right)}}}-{f{{\left({0}\right)}}}}}{{{3}-{0}}}}\)

\(\displaystyle={\frac{{{5}\cdot{3}-{5}\cdot{0}}}{{{3}}}}\)

\(\displaystyle={\frac{{{15}}}{{{3}}}}\)

\(\displaystyle={5}\)