3.15: Stationary points, sketch and number of roots

0606/22/F/M/25 — Question 2 · 9 marks

(a)
Find the xx-coordinates of the stationary points on the curve y=(x2−1)(3−2x)2y = (x^{2} - 1)(3 - 2x)^{2}.
[4]
(b)
On the axes, sketch the graph of y=(x2−1)(3−2x)2y = (x^{2} - 1)(3 - 2x)^{2}, stating the intercepts with the coordinate axes.
[3]
(c)
Find the values of kk for which the equation (x2−1)(3−2x)2=k(x^{2} - 1)(3 - 2x)^{2} = k has three real and distinct roots.
[2]