(i)[4]
Using the substitution $u = x^{\frac{1}{2}}$, or by any other suitable method, find the values of $x$ for which the curve $y = f(x)$ has stationary points.
(ii)[3]
Find $f''(x)$ and then, either from this or by another method, determine the type of each stationary point.
(iii)[4]
The curve $y = f(x)$ is said to pass through the point $(4, -7)$. Find $f(x)$.