post number 6

So let’s go through all the days of the week. Monday we had a test from the previous week. Tuesday we learned three theorems. Wednesday we learned Optimization. Thursday we had a quiz on what we learned Tuesday. Friday we continued with optimization.

WHAT I UNDERSTOOD THIS WEEK:

The 3 theorems that we learned on Tuesday were Mean Value Theorem, Rolle’s Theorem, and Extreme Value Theorem.
MEAN VALUE THEOREM-
Must be continuous and differentiable on closed interval [a,b]. Then there must be a number ‘C’ on the interval such that f’(c)=f(b)-f(a)/b-a, or in simpler terms, take the derivative of ‘C’ and set it equal to the slope of [a,b].

ROLLE’S THEOREM-
Must be continuous and differentiable on closed interval [a,b]. If f(a)=f(b), then there must be a number ‘C’ on [a,b] where f(c)=0.

EXTREME VALUE THEOREM-
Must be continuous on closed interval [a,b] and must contain a max and min.

I kind of put these out of order, but the EVT brings you to the Rolle’s Theorem. The MVT is just by itself.

WHAT I DIDN’T UNDERSTAND THIS WEEK:

Optimization is stretching out an equation.
We were given some steps to follow in our packets that she handed out with the notes for optimization, but for some reason I just don’t understand it at all.

STEPS-
1. Identify all quantities
2. Write an equation
3. Reduce equation
4. Determine domain of equation
5. Determine max/min values

I might not understand just because I didn’t have much practice, but I really don’t know. There’s a test on Tuesday and I just need some help, how to even start the problem all the way through to the end.