AP EAMCET · Maths · Application of Derivatives
If the function \(f(x)=a \sin (x)+\frac{1}{3} \sin (3 x)\) attains maximum value at \(x=\frac{\pi}{3}\), then \(a\) equals
- A 3
- B \(\frac{1}{3}\)
- C 2
- D \(\frac{1}{2}\)
Answer & Solution
Correct Answer
(C) 2
Step-by-step Solution
Detailed explanation
\(f(x)=a \sin x+\frac{1}{3} \sin 3 x\) \[ \begin{aligned} & \therefore f^{\prime}(x)=a \cos x+\frac{1}{3} \cos 3 x \cdot(3)\left\{\because \frac{d}{d x} \sin x=\cos x\right\} \\ & f^{\prime}(x)=a \cos x+\cos 3 x \\ & \end{aligned} \] \(\because\) At \(x=\frac{\pi}{3}, f(x)\) is…
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