 # Driven by tech advances and financial pressures,the number of surgeries performed in physicians' offices nationwide has been increasing over the years Ayaana Buck 2021-09-26 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 $f\left(t\right)=-0.00447{t}^{3}+0.09864{t}^{2}+0.05192t+0.8\left(0\le t\le 15\right)$ 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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1. [Graph]
2. We substitute t=1 (any number from (0,15)) into f'(t)'
${f}^{\prime }\left(1\right)=-\frac{1341{\stackrel{˙}{1}}^{2}-19728\stackrel{˙}{1}-5192}{100000}=0.23578$