Question:medium
The slope of the curve $y = e^x \cos x$, $x \in (-\pi, \pi)$ is maximum at:
The slope of the curve $y = e^x \cos x$, $x \in (-\pi, \pi)$ is maximum at:
Show Hint
To find the maximum of any quantity (like slope), always treat that quantity as a new function and find where its derivative is zero.
Updated On: May 2, 2026
- $x = \frac{\pi}{2}$
- $x = -\frac{\pi}{2}$
- $x = \frac{\pi}{4}$
- $x = 0$
- $x = \frac{\pi}{3}$
Show Solution
The Correct Option is D
Solution and Explanation
Was this answer helpful?
0
Top Questions on Application of derivatives
- If the function \( f(x) \), defined below, is continuous on the interval \([0,8]\), then: \[ f(x) = \begin{cases} x^2 + ax + b, & 0 \leq x < 2 \\ 3x + 2, & 2 \leq x \leq 4 \\ 2ax + 5b, & 4 < x \leq 8 \end{cases} \]
- BITSAT - 2024
- Mathematics
- Application of derivatives
- If \( x\sqrt{1 + y} + y\sqrt{1 + x} = 0 \), then find \( \frac{dy}{dx} \).
- BITSAT - 2024
- Mathematics
- Application of derivatives
- If \( y = \tan^{-1}\left( \frac{\sqrt{x} - x}{1 + x^{3/2}} \right) \), then \( y'(1) \) is equal to:
- BITSAT - 2024
- Mathematics
- Application of derivatives
- At \( x = \frac{\pi^2}{4} \), \( \frac{d}{dx} \left( \tan^{-1}(\cos\sqrt{x}) + \sec^{-1}(e^x) \right) = \)
- BITSAT - 2024
- Mathematics
- Application of derivatives
- Want to practice more? Try solving extra ecology questions todayView All Questions
