Applications Of Derivatives Question 349
Question: In $ (-4,,4) $ the function $ f(x)=\int\limits_{-10}^{x}{(t^{4}-4){e^{-4t}}dt} $ has
[AMU 2002]
Options:
A) No extrema
B) One extremum
C) Two extrema
D) Four extrema
Show Answer
Answer:
Correct Answer: C
Solution:
$ f(x)=\int_{-10}^{x}{(t^{4}-4){e^{-4t}}dt} $
therefore $ {f}’(x)=(x^{4}-4){e^{-4x}} $
Now $ {f}’(x)=0\Rightarrow x=\pm \sqrt{2},,\pm \sqrt{2} $
Now $ {f}’’(x)=-,4(x^{4}-4){e^{-4x}}+4x^{3}{e^{-4x}} $
At $ x=\sqrt{2} $ and $ x=-\sqrt{2} $ the given function has extreme value.
BETA
