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f(x)=integral{e^x(x-1)(x-2)dx. then f(x) decreases in what interval?

f(x)=integral{e^x(x-1)(x-2)dx.
then f(x) decreases in what interval?

Grade:12th pass

1 Answers

Nishant Vora IIT Patna
askIITians Faculty 2467 Points
7 years ago
Hi,

f(x)=integral{e^x(x-1)(x-2)dx.

So f’(x) = ex(x-1)(x-2)
Now for decreasing functions
f’(x) < 0
so f’(x) = ex(x-1)(x-2) <0

But ex is always positive
so (x-1)(x-2) <0
So x\epsilon (1,2) for this interval f is decreasing

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