Question

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

Answer 1

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.

$y'=6x^2+6x-12$

Next, find the zeros of y' by factoring.

$6(x^2+x-2)=0 \\ x = -2, x = 1$

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

$(-2,21), (1,-6)$