finding the slope of the tangent by differentiating the curve

According to the question, tangent is parallel to the x – axis , which implies m = 0

x = 3 or x = 2

since this point lies on the curve, we can find y by substituting x

y = 2(3)³ – 15(3)² + 36(3) – 21

y = 6

or

y = 2(2)³ – 15(2)² + 36(2) – 21

y = 7

equation of tangent is given by y – y₁ = m(tangent)(x – x₁)

y – 6 = 0(x – 3)

y = 6

or

y – 7 = 0(x – 2)

y = 7