2.62: Stationary points on a cubic composite curve

Find $\dfrac{\mathrm{d}y}{\mathrm{d}x}$ and $\dfrac{\mathrm{d}^{2}y}{\mathrm{d}x^{2}}$.

Find the exact value of the $x$-coordinate of each of the stationary points of the curve.

Use the second derivative test to determine the nature of each of the stationary points.