Calculus questions, need to figure out how to do these for my exam.?

Question

Alright, pretty simple, follow this link...http://www.ms.uky.edu/~ma123/exam2.xhtml

and its questions #8, 10, 11, 13. I missed those on the original exam, and our teacher didn't have time to go over them. Whomever answers the most, and gives me a general quick explanation of how they got the answer will get the 10 pts.

my Final exam. and once again, just a brief explanation, don't spend your entire day trying to work them out. You don't even have to give me the answers, you can just say how you would (or did) figure them out.

thanks santmann..

I'll make sure to give you the 10 pts as early as tomorrow. When I make an A on my test, I'll be sure to thank you. I can't believe I missed # 13, I need to start checking over my work after I take tests.

Answer 1

8)
4 is the slope of the tangent so g´(2)=4 and g(2) =-1 mesured on the tangent
h´(x) = x*g´(x)+g(x) so h´(2) = 2*4-1=7
10) g´(s) = -1/(s+1)^2 no roots
calculate g(s) at 0 and 2 g(0) =1 aand g(2) = 1/3 so the max is 1
11)
x<0 h´(x= 1+x = 0 x=-1 (no) x>0 h´(x) = 1-x x= 1
Inthe interval the derivative is positive ( except at 0 where it does not exist) so the maximum occurs at x=1

13mean variation is (A^3-0)/A= A^2
3s^2 at s=1 = 3 so A^2 = 3 and A = sqrt(3) taking the positive solution
Clear enough???