Search any question & find its solution
Question:
Answered & Verified by Expert
The point in the interval $[0,2 \pi]$, where $f(x)=e^x \sin x$ has maximum slope, is
Options:
Solution:
2693 Upvotes
Verified Answer
The correct answer is:
$\frac{\pi}{2}$
Hints: $f^{\prime}(x)=e^x(\sin x+\cos x)$
$$
\begin{aligned}
& f^{\prime \prime}(x)=e^x(\sin x+\cos x+\cos x-\sin x) \Rightarrow f^{\prime \prime}(x)=e^x \cos x=0 \\
& \Rightarrow x=\frac{\pi}{2}
\end{aligned}
$$
$$
\begin{aligned}
& f^{\prime \prime}(x)=e^x(\sin x+\cos x+\cos x-\sin x) \Rightarrow f^{\prime \prime}(x)=e^x \cos x=0 \\
& \Rightarrow x=\frac{\pi}{2}
\end{aligned}
$$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.