Mathematics

Problem

Let

g(x)=x^{2}\sin x-5x\cos x

. (i) Find

g'(x)

. (ii) Evaluate

g'\!\left(\dfrac{\pi}{2}\right)

. (iii) Using the result of part (ii), comment on the monotonic nature of

g(x)

in a neighbourhood of

x=\dfrac{\pi}{2}