Applications-Of-Derivatives Question 432
Question: The point in the interval $ (0,2\pi ) $ where $ f(x)=e^{x}\sin x $ has maximum slope is
Options:
A) $ \frac{\pi }{4} $
B) $ \frac{\pi }{2} $
C) $ \pi $
D) $ \frac{3\pi }{2} $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] Given $ f(x)=e^{x}\sin x $
$ \Rightarrow f’(x)=e^{x}\cos x+e^{x}\sin x $
$ \Rightarrow slope=e^{x}(\cos x+\sin x) $ Now, $ \frac{d}{dx}(\cos x+\sin x)=0 $
$ \Rightarrow -\sin x+\cos x=0 $
$ \Rightarrow \sin x=\cos x\Rightarrow \tan x=1 $
$ \Rightarrow x=\frac{\pi }{4} $
BETA
