1.1. A curve has equation $y={x}^{3}+2x+1.$

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

1.2. (i) Write down the value of x for which  $\frac{{d}^{2}y}{d{x}^{2}}=0$.

(ii) By considering the sign of  $\frac{{d}^{2}y}{d{x}^{2}}$  just either side of the value of x found in part (i), show that this is a point of inflection.

1.3. Hence, or otherwise, find the coordinates of the point of inflection on the curve with equation $y={x}^{3}+2x+1.$