Problem

The diagram shows the curve with equation $y = 2x^2 - \frac{5}{x} + 3$. The curve crosses the $x$-axis at the point $P(1, 0)$ and $M$ is a minimum point.

(a) Find the gradient of the curve at $P$.

(b) Find the coordinates of $M$. Give each coordinate correct to 3 significant figures.