91Ó°ÊÓ

Determine where the function is concave upward and where it is concave downward. $$ h(r)=-\frac{1}{(r-2)^{2}} $$

Lynbrook West, an apartment complex, has 100 two-bedroom units. The monthly profit (in dollars) realized from renting out \(x\) apartments is given by $$ P(x)=-10 x^{2}+1760 x-50,000 $$ To maximize the monthly rental profit, how many units should be rented out? What is the maximum monthly profit realizable?

Sketch the graph of the function, using the curve-sketching quide of this section. $$ f(t)=2 t^{3}-15 t^{2}+36 t-20 $$

Determine where the function is concave upward and where it is concave downward. $$ g(t)=(2 t-4)^{1 / 3} $$

Sketch the graph of the function, using the curve-sketching quide of this section. $$ h(x)=\frac{3}{2} x^{4}-2 x^{3}-6 x^{2}+8 $$

Sketch the graph of the function, using the curve-sketching quide of this section. $$ f(t)=3 t^{4}+4 t^{3} $$

The altitude (in feet) attained by a model rocket \(t\) sec into flight is given by the function $$ h(t)=-\frac{1}{3} t^{3}+4 t^{2}+20 t+2 \quad(t \geq 0) $$ Find the maximum altitude attained by the rocket.

Determine where the function is concave upward and where it is concave downward. $$ f(x)=(x-2)^{2 / 3} $$

Determine where the function is concave upward and where it is concave downward. $$ f(x)=\frac{e^{x}-e^{-x}}{2} $$

Data show that the number of nonfarm, full-time, self-employed women can be approximated by $$ N(t)=0.81 t-1.14 \sqrt{t}+1.53 \quad(0 \leq t \leq 6) $$ where \(N(t)\) is measured in millions and \(t\) is measured in 5 -yr intervals, with \(t=0\) corresponding to the beginning of 1963\. Determine the absolute extrema of the function \(N\) on the interval \([0,6]\). Interpret your results.