Help with the very last VCAA 2010 exam 2 q?

[ggxxx]

Q4f... anyone have any idea how to do it? D:

[vgardiy]

I subbed f(1)=1 in first, and figured out that either b=3 or a=1.
when b=3, a=1 which meant there was only one stationary point, which is incorrect.
so that means a=1. Then p corresponds to p=(b+1)/4 hence
f((b+1)/4=(b+1)/4
and solved that for b=15
(15+1)/4=p=4