Problem

The equation of a curve is $y=2x^2-3$. Two points $A$ and $B$ with $x$-coordinates $2$ and $(2+h)$ respectively lie on the curve.

(a) Find and simplify an expression for the gradient of the chord $AB$ in terms of $h$.

(b) Explain how the gradient of the curve at the point $A$ can be deduced from the answer to part (a), and state the value of this gradient.