Question:
The slope of the tangent to the curve \(y=e^x\cos x\) is minimum at \(x=\alpha,\;0\le\alpha\le2\pi\). Then the value of \(\alpha\) is
The slope of the tangent to the curve \(y=e^x\cos x\) is minimum at \(x=\alpha,\;0\le\alpha\le2\pi\). Then the value of \(\alpha\) is
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Min slope occurs when second derivative is zero.
Updated On: Mar 23, 2026
- \(0\)
- \(\pi\)
- \(2\pi\)
- \(3\pi/2\)
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The Correct Option is D
Solution and Explanation
Step 1: \[ \frac{dy}{dx}=e^x(\cos x-\sin x) \]
Step 2: Minimise derivative: \[ \frac{d^2y}{dx^2}=e^x(-2\sin x)=0 \Rightarrow x=\frac{3\pi}{2} \]
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