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

Answer 1

f'(x) is the slope of the tangent line

Horizontal line has slope = 0

So you need to solve f'(x) = 0

Using power rule, f'(x) = 6x² + 6x - 12 = 6 (x² + x - 2) = 6 (x+2) (x-1)

f'(x) = 0 when x = -2, 1

Required points will be ( -2, f(-2)) and (1, f(1))