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

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].

• Questions are typically answered in as fast as 30 minutes

### Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

l1koV

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