To start off the week we had a test on the first derivative test and second derivative test. The rest of the week consisted of doing some different things that I understand fully for once. One is the Rolles Theorem. And the other is the Mean Value Theorem. They are similar in a way that the equation has to be both continuous on a closed interval differentiable on an open interval in order to use both of these.
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.
But I am not clear at all on optimization. Once I get started I can get most of it but it is getting started that is killing me. So if there is any way someone can help me it would be appreciated. And also I had no idea how to even think about starting the last problem on the first derivative and second derivative tests test if someone can help me for future reference.
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You figure out your secondary and primary equations then find a variable in your secondary and plug into your primary simplfy that and take the derivative set equal to 0 and solve for x then you find another unkown varbile and plug both varibles you got into the original and get your final awnser
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