Math 111 - Sept 7, 2011
Test Monday, Sept 12, [1.1,2.2]
2.1) Increasing/Decreasing, Piecewise functions...
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 (instantaneously) constant at
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?
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: