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If the function e^(-x) f(X) assumes its ...

If the function `e^(-x)` f(X) assumes its minimum in the interval [0,1] at `x = 1//4` which of the following is true ?

A

`f'(x)ltf(X),1//4ltxlt3//4`

B

`f'(x)gtf(X),0ltxlt1//4`

C

`f'(x)ltf(X),0ltxlt1//4`

D

`f'(x)ltf(X),3//4ltxlt1`

Text Solution

Verified by Experts

The correct Answer is:
3
Let `g(X)=e^(-x)f(x)`
As `g(x)0 g(x)` is increasing
So for `xlt1/4g(X)ltg(1/4)=0 or f(x)-f(x)e^(-x)lt0`
or `f(x)ltf(x)in (0,1//4)`
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