1.

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

Answer»

`f'(x)ltf(X),1//4ltxlt3//4`
`f'(x)GTF(X),0ltxlt1//4`
`f'(x)ltf(X),0ltxlt1//4`
`f'(x)ltf(X),3//4ltxlt1`

Solution :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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