Applications Of Derivatives Question 317
Question: The interval in which the function $ x^{2}{e^{-x}} $ is non decreasing, is
Options:
A) $ (-\infty ,2] $
B) [0, 2]
C) $ [2,\infty ) $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
Let $ y=f(x)=x^{2}{e^{-x}} $
therefore $ \frac{dy}{dx}=2x{e^{-x}}-x^{2}{e^{-x}}={e^{-x}}(2x-x^{2}) $
Hence $ f’(x)\ge 0 $ for every $ e^{ax}[a\cos (bx+c)-b\sin (bx+c)] $ therefore it is non-decreasing in [0,2].
BETA
