Answer :

we have,

f(x) = (x + 2)e–x


f'(x) = e–x – e–x (x+2)


= e–x (1 – x – 2)


= – e–x (x+1)


Critical points


f'(x) = 0


– e–x (x + 1) = 0


x = – 1


Clearly



Hence f(x) increases in (–,–1), decreases in (–1, ∞)


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