Find the points on the curve y = 2x3 + 3x2 − 12x + 6 where the tangent line is horizontal.

N.b., this is copied from an answer I wrote for someone else.

Thinking about the graph of y, the rate of change is zero whenever there is an extremum.

First, differentiate y.



Next, find the zeros of y' by factoring.



Now, we substitute these x-values into the original equation to find the coordinates.