1.

Let f(X)=In (2x -x^2)+ sin (pix)/(2). Then which one of the following options is not correct?

Answer»


Solution :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 rArr2^(-)`
minmum values of the function f(x) does not EXIST
HENCE ,option (b) is not correct


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