The function ` f(x) = a sin x + 1/3 sin 3x` has maximum value at ` x = pi/3` , the value of a is

Options

A. 3
B. `1/3`
C. 2
D. `1/2`

Answer

C

Explanation

We have, ` f(x) = a sin x + 1/3 sin 3x f'(x) = a cos x = a sin x + cos 3x`
Since f(x) has maximum value at
since, f(x) has maximum value at
` x = pi/3`
` f'(pi/3) = 0`
` Rightarrow f'(pi/3) = a cos pi/3 + cos 3 xx pi/3 = 0`
` = a/2 -1 =0`
` Rightarrow a=2`