trina's 6th post

This first week of calculus started off easy when we learned about Rolle's theorum and the Mean Value theorum. When using Rolle's theorum you are given an equation and a point. First you figure out if the function is continuous and differentiable. If it is not continuous or differentiable on the point give, then the problem cannot be worked. If it is continuous and differentiable, then you can move on to the next steps.

Let's say they give you x^2-2x and (0,2) you would first plug in
f(0)=0^2-2(0)=0
f(2)=(2)^2-2(2)=0

The y values have to match, if they do not the problem cannot be worked further.

Now you take the derivative of the function and set it equal to the y value 0
2x-2=0
which gives you x=1. Therefor c=1


In Mean Value theorum, you still check for continuous and differentiability.
x^3 and (0,1)

first you plug into the formula like Rolle's
so f(0)= 0^3=0
f(10= 1^3=1

then you plug into the formula to find the slope between the two points: f(b)-f(a)/b-a
so then you plug in: 1-0/1-0=1

now you take the derivative of the function and set equal to the slope
3x^2=1

which will give you x= +or- 1/3, but c will equal 1/3 because it is positive and (0,1) is positive.


What i did not understand this week is optimization. Once some were worked in class, i started to get the feel on how to do it, but i do not know how to distinguish from primary functions and when to plug in different numbers to different functions. If anyone can help me with this it would be a big help. Thanks :)