# Find the average rate of change of the function f(x)=5x from x_{1}=0

Find the average rate of change of the function $$\displaystyle{f{{\left({x}\right)}}}={5}{x}$$ from $$\displaystyle{x}_{{{1}}}={0}$$ to $$\displaystyle{x}_{{{2}}}={3}$$.

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Clara Reese

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
$$A(x)=\frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1}}$$
$$\displaystyle={\frac{{{f{{\left({3}\right)}}}-{f{{\left({0}\right)}}}}}{{{3}-{0}}}}$$
$$\displaystyle={\frac{{{5}\cdot{3}-{5}\cdot{0}}}{{{3}}}}$$
$$\displaystyle={\frac{{{15}}}{{{3}}}}$$
$$\displaystyle={5}$$