Question

Critical points of x+5/x+2>0

Answer 1

{-5, -2}

Explanation:

In a case like this please use parentheses to remove ambiguities. If I were to take your "x+5/x+2" literally, I'd have to write x plus 5/x plus 2.

I suspect that you actually meant (x + 5) / (x + 2), and will start with that.

First of all, this function is not defined at x = -5 or at x = -2. Thus, -5 and -2 are critical points.

Secondly, there may be one or more critical points beyond this. To find out, we have to differentiate (x+5)/(x+2):

(x + 2)(1) - (x + 5)(1)

f '(x) = ------------------------------

(x + 2)

Here it's clear that x cannot = -2, which would cause division by zero.

Thus, our critical values are {-5, -2}.