Math 111 - Sept 7, 2011

Test Monday, Sept 12, [1.1,2.2]

Solve for

2.1) Increasing/Decreasing, Piecewise functions...

Increasing/Decreasing...

Positive slope is increasing (up as you go left-to-right)

Negative slope is decreasing (down as you go left-to-right)

Is decreasing remember vertex of a parabola is at

Is increasing

Is (instantaneously) constant at

increasing:

decreasing:

relative mimimum:

relative maximum:

A farmer wants to make 2 pens like this:

She has 100' of fence and wants the pens to be as large (in area) as possible. What should the dimensions of the pens be?

constrained by

Solve the second equation for L or W...

Plug that into the thing you want to max(min)imize

Where does this change from increasing to decreasing???

It's just a parabola so the vertex is at:

You have 10" wide sheet metal that you will fold into a U shaped gutter like:

What dimensions will carry the most water?

Maximize constrained by

Solve for w or h:

Plug into first:

Which is a parabola with vertex:

Piecewise functions: