Question

find critical points of (x+1)/(x^(2)+1)

Answer 1

i got the derivative as [(x^(2)+1)-(-2x^(2)+2x)]/[(x^(2)+1]^2

Answer 2

Then you need to take that and make it equal 0. Find just when the top = 0. Then look for the bottom and if any of the answers match then they are holes.

(x+3)(x-5)
__________ =0
(x-5)

x=-3 and 5. But if x =5 then the bottom = 0 and therefore that isn't answer.

Answer 3

so you first solve numerator=0 and then denominator=0? and for this one there are no critical points right?

Answer 4

@malical

Answer 5

First off it looks like your derivative is wrong.

Denominator(derivative numerator)-(numerator)(derivative denominator)
over
denominator squared.

If you did do this correctly I'm sorry. I didn't actually work it out, it just smelled wrong to me.