Mathematics | VITEEE 2017 | Discussion Page

The difference between greatest and least value of f(x) = 2 sin x + sin 2x, x Ε [0, 3π/2] is

A) $\frac{3\sqrt{3}}{2}$

B) $\frac{3\sqrt{3}}{2}-2$

C) $\frac{3\sqrt{3}}{2}+2$

D) None of these

Option C

f(x) = 2 sin x + sin 2x

f'(x) = 2 cos x + 2 cos 2x = 2 (cos x + cos 2x)

.'. f'(x) = 0 → 2cos²x+ cosx - 1 = 0

Cos x = $ \frac{-1\pm3}{4}$ = -1, 1/2 .'. x = π, π/3

Now, f(0) = 0, f (3π/2) = -2

f(π) = 0, f (π/3) = $\frac{2\sqrt{3}}{2}$ + $\frac{\sqrt{3}}{2}$ = $\frac{3\sqrt{3}}{2}$

.'. difference between greatest value and least value = $\frac{3\sqrt{3}}{2}+2$

Discussion Forum