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The value of a for which the function f(...

The value of `a` for which the function `f(x)=asinx+(1/3)sin3x` has an extremum at `x=pi/3` is (a) 1 (b) `-1` (c) 0 (d) 2

A

1

B

-1

C

0

D

2

Text Solution

Verified by Experts

The correct Answer is:
D
If f(x) has an ectremum at ` x=pi//3`, then
`f'(x)=0 " at " x=pi//3`.
Now , `f(x) =asinx+1/3sin3x`
`rArr f'(x) =acosx+cos3x`
`therefore f'(pi//3)=0rArr acos(pi//3)+cospi=0rArra=2`
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