A curve has equation $2x^3-3x^2-12x+12$

Differentiate the function to obtain $\frac{dy}{dx}$

a$)$ Find the $x$ coordinates of the points where $\frac{dy}{dx}=0$ and hence the coordinates of the turning points on the curve.

b$)$ With the aid of a table consider the sign of $\frac{dy}{dx}$ on either side of the turning points, determine whether the turning points are maximum or minimum points.

c$)$ Sketch the curve showing the turning points clearly and label any other points of interest.