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

abondantQ 2021-09-16 Answered
Find the average rate of change of the function \(\displaystyle{f{{\left({x}\right)}}}={5}{x}\) from \(\displaystyle{x}_{{{1}}}={0}\) to \(\displaystyle{x}_{{{2}}}={3}\).
The average rate of change is _______. (Simplify your answer.)

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Expert Answer

Clara Reese
Answered 2021-09-17 Author has 15452 answers

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

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