Question

How do I find the critical points?

Answer 1

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:

$\frac{d}{dx}(x^{2} - 1)^{3}$

So we apply chain rule:

= $3(x^{2} - 1)^{2} * 2x$

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