Mathematics

Problem

For the function

p(x)=x^{3}\sin x

: (a) Determine

p'(x)

, leaving your final answer with powers of

x

collected and a single trigonometric factor in each term. (b) Factorise

p'(x)

completely. (c) Show that

p'(x)=x^{2}(3\sin x + x\cos x)

and hence find all

x

0\le x\le 2\pi

for which the tangent to

y=p(x)

is horizontal.