Calculate the average rate of change for the function f(x)=x^2+x-12, over the interval: 1. [0,3] 2. [-1,10]

Cheyanne Leigh 2021-09-05 Answered
Calculate the average rate of change for the function \(\displaystyle{f{{\left({x}\right)}}}={x}^{{2}}+{x}-{12}\), over the interval:
1. [0,3]
2. [-1,10]

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Expert Answer

stuth1
Answered 2021-09-06 Author has 25204 answers

\(\displaystyle{f{{\left({x}\right)}}}={x}^{{2}}+{x}-{12}\)
1. \(\displaystyle\frac{{{f{{\left({b}\right)}}}-{f{{\left({a}\right)}}}}}{{{b}-{a}}}=\frac{{{\left({3}^{{2}}+{3}-{12}\right)}-{\left({0}^{{2}}+{0}-{12}\right)}}}{{{3}-{0}}}\)
\(=4\)
2. \(\displaystyle\frac{{{f{{\left({b}\right)}}}-{f{{\left({a}\right)}}}}}{{{b}-{a}}}=\frac{{{\left({10}^{{2}}+{10}-{12}\right)}-{\left({\left(-{1}\right)}^{{2}}+{\left(-{1}\right)}-{12}\right)}}}{{{10}-{\left(-{1}\right)}}}\)
\(=10\)

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