Week 7

Wow, I cannot believe we are already in the seventh week of school. It seems like just yesterday we were walking into the first day of class scared of how hard calculus may be. Anyways, this week we reviewed optimization on Monday and Tuesday. On Wednesday we had a quiz on optimization and recieved our review packets for exams. On Thursday we had a field trip, and on Friday we worked on our packets.

So far I have understood most of the things in our packets.

I understand how to take derivatives.
Example:
9xsin+4cox

you would use product and rule and the addition property to solve this problem.

= [9x(cosx) + sinx(9)] + 4(-sinx)
= 9xcosx + 5sinx

I also understand that slope is the same thing as derivative

I have recently discoved that a higher-order derivative is just that you keep taking derivatives until you are told to stop.
Example:
f ''(x) = 2x^(7/5), find f^(iv)(x)
first you would take the derivative of f ''(x) and get (14/5)x^(2/5). Then you would take the derivative of that to get (28/25)x^(-3/5).

Also, if it tells you to find a derivative a certain point, then take the derivative and plug the point in for x.


We copied down the Intermediate Value Theorem on Friday. I do not know how to solve a problem with it.
Example:

Find the value of c guaranteed by the Intermediate Value Theorem.
f(x) = x^2 - 2x - 3, [4,8], f(c) = 12.

Can anybody help me with that? Thanks.