(a)[2]
Find $\frac{dy}{dx}$ and $\frac{d^2y}{dx^2}$ in terms of $k$.
(b)[4]
It is given that $k = 2$. Find the coordinates of the stationary point and determine whether it is a maximum or minimum.
(c)[6]
The points $A$ and $B$ on the curve have $x$-coordinates $0.25$ and $1$ respectively. For another value of $k$, the tangents to the curve at $A$ and $B$ intersect at a point whose $x$-coordinate is $0.6$. Find this value of $k$.