I have an exam tomorrow and need help with this problem to make sure I understand the material...
Determine the y-coordinate of the critical point for f(x)=1/x+1/5-x

Question

anonymous · Answer

Did you take the derivative?

anonymous · Answer

yea i got $$f'(x)=-1/x^2+1/(5-x)^2$$

anonymous · Answer

Looks right. So where would this function be 0?

anonymous · Answer

ummm this is where i get stuck...could i try to get x's on one side

anonymous · Answer

Well, I think he means the function will have its critical point at f'(x) = 0.
Just do 1/x^2 = 1/(5-x)^2, got it?

anonymous · Answer

then would you cross multiply...???

anonymous · Answer

See, if 1/x^2 = 1/(5-x)^2, then x^2 = (5-x)^2. (x^2)^1/2 = ((5-x)^2)^1/2
|x| = |5-x|
x = 5/2 or -5 = 0... since -5 is not 0, x = 5/2.

anonymous · Answer

ok i see