Question

The difference between the greatest and least values of the function y = cos x + $\frac{1}{2}$cos 2x – $\frac{1}{3}$cos 3x is –

• A. 2/3
• B. 9/4
• C. 4/9
• D. None

Answer 1

Answer: (B)

9/4

Answer 2

f(x) = – sin x – sin 2x + sin 3x

⇒ – 4 sin x sin 3/2x sin x/2 = 0

x = 0, π, 2π, $\frac{2\pi}{3}$, $\frac{4\pi}{3}$are critical point.

X	0	π	2π	2π/3	4π/3
f(x)	7/6	–1/6	7/6	–13/12	–13/12

differential is = 7/6 – (–13/12) = 9/4