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Mathematics
The function f(x)=x5 e-x is increasing in the interval
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Q. The function $f(x)=x^5 e^{-x}$ is increasing in the interval
KEAM
KEAM 2022
A
$(5, \infty)$
B
$(4, \infty)$
C
$(-4, \infty)$
D
$(-\infty, 5)$
E
$(-5, \infty)$
Solution:
$ f^{\prime}(x)=5 x^4 e^{-x} x^5 e^{-x}$
$ =e^{-x} x^4(5-x)$
$ (-\infty, 5)$