AP EAMCET · Maths · Application of Derivatives
The value of ' \(a\) ' for which the function \(f(x)=a \sin x+\frac{1}{3} \sin 3 x\) has an extremum value at \(x=\frac{\pi}{3}\) is
- A 1
- B -1
- C 0
- D 2
Answer & Solution
Correct Answer
(D) 2
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { } \because f(x)=a \sin x+\frac{1}{3} \sin 3 x \\ & f(x)=a \cos x+\frac{1}{3} \times 3 \cos 3 x \\ & \Rightarrow f(x)=a \cos x+\cos 3 x \\ & \because f(x) \text { has an extremum at } x=\frac{\pi}{3} \\ & \therefore a x \cos…
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