Driven by technological advances and financial pressures, the number of surgeries performed in physicians' offices nationwide has been increasing over

banganX 2021-05-31 Answered

Driven by technological advances and financial pressures, the number of surgeries performed in physicians' offices nationwide has been increasing over the years. The function \(\displaystyle{f{{\left({t}\right)}}}=-{0.00447}{t}^{{{3}}}+{0.09864}{t}^{{{2}}}+{0.05192}{t}+{0.8}{\left({0}\leq{t}\leq{15}\right)}\) gives the number of surgeries (in millions) performed in physicians' offices in year t, with \(t=0\) corresponding to the beginning of 1986.
a. Plot the graph of f in the viewing window \([0,15]\times [0,10]\).
b. Prove that f is increasing on the interval [0, 15].

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l1koV
Answered 2021-06-01 Author has 12617 answers

1. [Graph]
2. We substitute \(t=1\) (any number from (0,15)) into f'(t)'
\(\displaystyle{f}'{\left({1}\right)}=-{\frac{{{1341}\dot{{1}}^{{{2}}}-{19728}\dot{{1}}-{5192}}}{{{100000}}}}={0.23578}\)

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Driven by technological advances and financial pressures, the number of surgeries performed in physicians' offices nationwide has been increasing over the years. The function \(\displaystyle{f{{\left({t}\right)}}}=-{0.00447}{t}^{{{3}}}+{0.09864}{t}^{{{2}}}+{0.05192}{t}+{0.8}{\left({0}\leq{t}\leq{15}\right)}\) gives the number of surgeries (in millions) performed in physicians' offices in year t, with t=0 corresponding to the beginning of 1986.
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