Find the critical numbers of the function.?

Question

f(x)= (x+1)/(x^2+z+1)

there should be 2... i know one is 0, but I can't figure out the other one. I thought it would be -1, but it's not.

Answer 1

if f(x) is as above - have fun for I cannot tell if you are into complex numbers or perhaps z is some unassigned constant [not variable like x]

if you made a typo/brain-fart reading your own notes and you meant :

f(x) = (x+1) / (x^2 + 2 + 1)
then
f(x) = (x+1) / (x+1)^2 = 1 / (x+1)

so yes -1 is a critical point as f(x) is "undefined" there

Answer 2

Do you really mean z in the denominator?

f'(x) = [(x^2+z+1) - (x+1)(2x)]/(x^2+z+1)^2
= [-x^2+z+1- 2x] / (x^2+z+1)^2

To find the critical numbers, use the quadratic formula to find the roots of the numerator.