A curve is given by

1. Find the coordinates of the stationary point of the curve.

2. Find the coordinates of the point of inflection of the curve.

3. A student believes that

   For any curve, if $\frac{dy}{dx}=0$ at some point, then the curve has a turning point at that point.

   Explain, by drawing an appropriate diagram, why

   $$y=x^3-6x^2+12x-6$$

   is a counterexample to this claim.