Applications Of Derivatives Question 416
Question: The function $ f(x)=\frac{x^{2}}{e^{x}} $ monotonically increasing if
Options:
A) x < 0 only
B) x > 2 only
C) 0 < x < 2
D) $ x\in (-\infty ,0)\cup (2,\infty ) $
Show Answer
Answer:
Correct Answer: C
Solution:
[c] $ f(x)=\frac{x^{2}}{e^{x}};f’(x)=\frac{2x.e^{x}-e^{x}.x^{2}}{{{( e^{x} )}^{2}}} $
$ f’(x)=\frac{2x-x^{2}}{e^{x}} $ As $ e^{x} $ is always positive and for monotonically increasing; $ 2x-x^{2}>0 $
$ \Rightarrow x^{2}-2x<0\Rightarrow x(x-2)<0\Rightarrow x\in (0,2) $
BETA
