Critical points is where the derivative (slope) is zero or does not exist. So to do this we have to find the derivative of our function:
[tex] \frac{d}{dx}(x^{2} - 1)^{3} [/tex]
So we apply chain rule:
= [tex]3(x^{2} - 1)^{2} * 2x[/tex]
Set our first derivative to zero and solve for x:
3(x^2 - 1) * 2x = 0
So we can see that (by plugging in) 0, -1 and 1 makes our solution true
So our critical value is x = 0, x = -1, x = 1
