1.16: Stationary points of a cubic curve

4PM1/1R/November/2020 — Question 4 · 6 marks

The curve C\displaystyle C has equation
y=x33x224x+6.y=x^3-3x^2-24x+6.
(a) Use calculus to find the coordinates of each of the stationary points on C\displaystyle C.
(4)
(b) Determine the nature of each of these stationary points. Justify your answers.
(2)