91Ó°ÊÓ

The U.S. Postal Service will accept a package if its length plus its girth (the distance all the way around) does not exceed 84 inches. Find the dimensions and volume of the largest package with a square base that can be mailed.

Find (without using a calculator) the absolute extreme values of each function on the given interval. \(f(x)=3 x^{2}-x^{3}\) on \([0,5]\)

Marine ecologists estimate the reproduction curve for swordfish in the Georges Bank fishing grounds to be \(f(p)=-0.01 p^{2}+5 p\), where \(p\) and \(f(p)\) are in hundreds. Find the population that gives the maximum sustainable yield, and the size of the yield.

Use implicit differentiation to find \(d y / d x\). \(x y-x=9\)

Use implicit differentiation to find \(d y / d x\). \(x^{3}+2 x y^{2}+y^{3}=1\)

A homeowner wants to build, along his driveway, a garden surrounded by a fence. If the garden is to be 800 square feet, and the fence along the driveway costs $$\$ 6$$ per foot while on the other three sides it costs only $$\$ 2$$ per foot, find the dimensions that will minimize the cost. Also find the minimum cost.

Find (without using a calculator) the absolute extreme values of each function on the given interval. \(f(x)=6 x^{2}-x^{3}\) on \([0,5]\)

Find the critical numbers of each function. \(f(x)=\left(x^{2}+6 x-7\right)^{2}\)

For each function: a. Make a sign diagram for the first derivative. b. Make a sign diagram for the second derivative. c. Sketch the graph by hand, showing all relative extreme points and inflection points. \(f(x)=x^{4}+8 x^{3}+18 x^{2}+8\)

The reproduction function for the Hudson Bay lyn \(x\) is estimated to be \(f(p)=-0.02 p^{2}+5 p\) where \(p\) and \(f(p)\) are in thousands. Find the population that gives the maximum sustainable yield, and the size of the yield.