How to find the local maximum/minimum of a polynomial function

any example used would suffice

y = 2x^3 - 15x^2 - 36x + 22

Take the first derivative:

dy/dx = 6x^2 - 30x - 36......Set this equal to 0.

6x^2 - 30x - 36 = 0.............Divide both sides by 6.

x^2 - 5x - 6 = 0....................Factor

(x - 6) * (x + 1) = 0

The critical points are x = 6 and x = -1

But which is the maximum and which the minimum?

Take the second derivative.

This was the first derivative dy/dx = 6x^2 - 30x - 36

So d^