Find the points on the curve y = 2x^3 + 3x^2 - 12x + 1 where the tangent is horizontal

Answer 1

That means the slope of the tangent is zero. Look for the points where the derivative
dy/dx = 6x^2 + 6x -12 = 0

x^2 +x -2 = 0
(x+2)(x-1) - 0

x - -2 or +1.