1.1. The curve C has equation  $y=3{x}^{3}+6{x}^{2}-5x+1.$

Find expressions for  $\frac{dy}{dx}$  and  $\frac{{d}^{2}y}{d{x}^{2}}$.

1.2. (i) Evaluate  $\frac{dy}{dx}$  and  $\frac{{d}^{2}y}{d{x}^{2}}$  when  $x=\frac{1}{3}$.

(ii) What does your answer to part (b) tell you about curve C at the point where  $x=\frac{1}{3}$?