Differentiation Question 388
Question: The nth derivative of $ xe^{x} $ vanishes when
[AMU 1999]
Options:
A) $ x=0 $
B) $ x=-1 $
C) $ x=-n $
D) $ x=n $
Show Answer
Answer:
Correct Answer: C
Solution:
$ f(x)=xe^{x} $
$ {f}’(x)=e^{x}+xe^{x} $
$ {f}’’(x)=e^{x}+e^{x}+xe^{x}=2e^{x}+xe^{x} $
$ {f}’’’(x)=2e^{x}+e^{x}+xe^{x}=3e^{x}+xe^{x} $
$ f^{n}(x)=ne^{x}+xe^{x} $ . Now, $ f^{n}(x)=0 $
Therefore $ ne^{x}+xe^{x}=0 $
Therefore $ x=-n $ .
BETA
