# How do you identify all the critical points for # x^2 – x + y^2 + y = 0#?

##### 1 Answer

Nov 2, 2016

#### Answer:

Please see the explanation for a description of how one does it.

#### Explanation:

Use implicit differentiation, to find the first derivative,

Separate

The critical points occur when the first derivative is equal to zero:

Find the two values of y where this occurs:

check the discriminant:

The critical points are