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

Driven by technological advances and financial pressures, the number of surgeries performed in physicians' offices nationwide has been increasing over the years. The function $f\left(t\right)=-0.00447{t}^{3}+0.09864{t}^{2}+0.05192t+0.8\left(0\le t\le 15\right)$ 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] $×$ [0,10].
b. Prove that f is increasing on the interval [0, 15].

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