In general, you solve questions of cancavity by looking at the second derivative. It will be negative where the function is concave downward. (It will be positive for concave upward, and zero at points of inflection.)
I find it convenient to get guidance from a graphing calculator.
f(x) is concave downard on the interval (-∞, 2).
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The derivative is
.. f'(x) = e^-x -x*e^-x
The second derivative is
.. f''(x) = -e^-x -(e^-x -x*e^-x)
.. = (x -2)*e^-x
This will be negative for x < 2.