Sec 4.5 Optimization and Modeling

Ex) Find the dimensions of the right cone that has a volume of 100 cubic inches and uses the minimum amount of material to build.

No top.

Volume of cone =

Surface area of cone =

Ex) Form a right triangle with one vertex at the origin, one vertex on the curve for x > 0 and one vertex on the x – axis at .

For what value of x is the area of this triangle a maximum?

Ex) You are in a race to get from point A to point B.

When running along the sides of the basin of goop, you move

at a rate of 5 ft/sec.

When moving through the goop, you move at a rate of 2 ft/sec.

Determine the path that optimizes your chances of winning.