3.103: Stationary points and sketch of a cubic factorisation

0606/12/O/N/24 — Question 2 · 9 marks

It is given that y=f(x)y = f(x) where f(x)=x(x−5)(1−2x)f(x) = x(x - 5)(1 - 2x).
(a)
Find the coordinates of the stationary points on y=f(x)y = f(x).
[4]
(b)
Sketch y=f(x)y = f(x), stating intercepts with the axes.
[3]
(c)
Hence find the values of kk for which f(x)=kf(x) = k has exactly one solution.
[2]