WBJEE · Maths · Application of Derivatives
The point in the interval \([0,2 \pi]\), where \(f(x)=e^x \sin x\) has maximum slope, is
- A \(\frac{\pi}{4}\)
- B \(\frac{\pi}{2}\)
- C \(\pi\)
- D \(\frac{3 \pi}{2}\)
Answer & Solution
Correct Answer
(B) \(\frac{\pi}{2}\)
Step-by-step Solution
Detailed explanation
Hints: \(f^{\prime}(x)=e^x(\sin x+\cos x)\) \[ \begin{aligned} & f^{\prime \prime}(x)=e^x(\sin x+\cos x+\cos x-\sin x) \Rightarrow f^{\prime \prime}(x)=e^x \cos x=0 \\ & \Rightarrow x=\frac{\pi}{2} \end{aligned} \]
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