3. If f(x)=

[Pages:3]math455feb222016.notebook

February 22, 2016

hw due Tuesday : Foerster p. 521#15 (review related rates) p. 526 #1 p. 531 #7 Optimization quest Friday Do Now:

2. If

3. If f(x)= a)

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February 22, 2016

Back to optimization:

1. What is the area of the largest rectangle that can be inscribed under the graph of

y = 2cosx for

?

2. A physical fitness room consists of a rectangle with a semicircle on each end. A 200 meter running track runs around the outside of the room.

Draw a diagram, let x and y represent the length and width of the rectangle.

Write the area A as a function of x.

(Using calculus) Find the dimensions of the rectangle that will maximize the area of the room. Verify your answer by graphing y=A(x).

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February 22, 2016

3. You are deciding on how to package a soft drink. The package will hold 22 cu in. of liquid. (about 12 fluid ounces). The package needs to be in the shape of a cylinder. What should the dimensions of the cylinder be so that you will use the least amount of material? (we will ignore that perhaps the bottom needs to be thicker than the sides)

Why are we using 22 as the volume and not 12? Does it matter?

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