2nd post for the holidays

Well I finally have my internet back up and working so I will do the last two blogs I have left to do. I will start with related rates. The steps for related rates are:
1. Identify all of the variables and equations
2. Identify the things that you are looking for
3. Sketch a graph and then label that graph
4. Create and write an equation using all of the variables
5. Take the derivative of this equation with respect to time
6. Substitute everything back in
7. Solve the equation

Next I will explain the Rolle's and Mean Value Theorem.
Rolle's
In Rolle's f(a)=f(b) or it can not be done. And there is always at least one answer which is "c". But mainly the way to do Rolle's is to start off making sure the equation is continuous and differentiable. Then make sure f(a)=f(b). Next take the derivative and solve for x. And finally pick the answer that falls between the interval given.

Mean Value
First you find the slope and plug into f(b)-f(a)/b-a. Then take the derivative and set it equal to the slope and solve for x. Finally take the answer between the interval given in the problem.

Now I am going to explain one of the first things we learned which is product and quotient rule.

Product rule is copy the first times the derivative of the last plus copy the first times the derivative of the second.

Quotient rule is copy the bottom times derivative of the top minus copy the top times the derivative of the bottom all divided by the bottom squared.

For my question I still cannot finish an optimization problem. I can start the problems I just cannot finish them.