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brandonholden
01.02.2020 •
Mathematics
For what intervals is f(x)=xe^-x concave down?
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Ответ:
f(x) = xe^-x
f '(x) = e^-x - xe^-x
f '' (x) = - e^-x - [e^-x - xe^-x] = -e^-x - e^-x + xe^-x = -2e^-x + xe^-x
f ''(x) = e^-x [x - 2]
Found x for f ''(x) < 0
e^-x [x -2] < 0
Given that e^-x is always > 0, x - 2 < 0
=> x < 2
Therefore, the function is concave downward in (- ∞ , 2)
Ответ:
ofc (you don’t need one)
Step-by-step explanation: