A) 1
B) \[-1\]
C) 0
D) 2
Correct Answer: D
Solution :
Key Idea: The extremum point of a function in which \[f(x)=0.\] We have \[f(x)=a\sin x+\frac{1}{3}\sin 3x\] \[\Rightarrow \] \[f(x)=a\cos x+\cos 3x\] Since, it is given that at \[x=\frac{\pi }{3},f(x)\]is extremum. i.e., \[f\left( \frac{\pi }{3} \right)=0\] \[\Rightarrow \]\[a\cos \left( \frac{\pi }{3} \right)+\cos 3\left( \frac{\pi }{3} \right)=0\] \[\Rightarrow \] \[a\left( \frac{1}{2} \right)+(-1)=0\] \[\Rightarrow \] \[a=2\]You need to login to perform this action.
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