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Let f(x)=In (2x-x^(2))+"sin"(pix)/(2). T...

Let `f(x)=In (2x-x^(2))+"sin"(pix)/(2).` Then

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Verified by Experts

The correct Answer is:
B
Clearlyf(x) id defined for all `x in (0,2)`
Also `f(1+alpha)=f(1-alpha)for all alpha in (0,1)`
So ,y =f (x) is symmetircal about the line x=1
Clearly `2 x-x^2` and sin `(pix)/(2)` attain the maximum value 1 at
x=1
Therefore `f(x)=In(2x-x^2)+sin (pix)/(2)` attains its maximum
value at x=1 .Also
We observe that `f(x) rArr - oo as x rArr 0^(+) or x rArr 2^(-)`
minmum values of the function f(x) does not exist
Hence ,option (b) is not correct
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