how to locate and classify the maximum and minimum values of the function y= 4x^3 + 3x^2 - 60x - 12.

as far as I know that at a stationery point dy/dx = 12x² + 6x – 60 =0

You can start the solution of the first derivative by

**noting the common factor** and dividing it out:

. . . . .
Then you solve the quadratic by

**factoring** or else by

**the Quadratic Formula**.

I don't know what tools you have at that point. You'll either need to find the sign of the derivative between the stationary (or "critical") points, or else apply the Second Derivative Test. (Or you can work straight from your knowledge of

**what positive cubics look like** to classify the two points in question.)