Question

Find all open intervals on which f(x)=x/(x^2+x-2) is decreasing. I found that f'(x)=-(x^2+2)/(x^2+x-2)^2 but what do I do after that?

Answer 1

So when a function is decreasing it's derivitive is negative, so you simply set the inequality \[\frac{ -(x ^{2}+2) }{ (x ^{2}+x-2)^{2} } < 0\]

Answer 2

So is the answer (negative infinity, -2)U(-2, 1)U(1, infinity)?

Answer 3

Correct

Answer 4

Thank you.

Answer 5

np