Question

Prove that value of sin² x (1 + cosx) is maximum x = 1/2.

Answer 1

Let y = sin²  x.(1 + cosx) …..(1)

Diff.wrt.x,

⇒ dy/dx = sin² x(- sin x) + (1 + cos x)

⇒ dy/dx = sinx (-sin² x + 2 cos x + 2 cos² x) …..(2)

For maxima of minima dy/dx= 0

Hence, at cos x = 1/3 function has maximum value.