Answer :

Let ………(i)


Taking logarithm on both sides we get




Now applying first derivative, we get



Now applying the product rule of differentiation we get



Now applying the derivative we get








Substituting the value of y from equation (i), we get



Now we will find the critical point by equating equation (i) to 0, we get



as cannot be equal to 0



But 1=log e1



Equating the terms we get




Hence f(x) has a stationary point at .


i.e the maximum value of


So the correct option is option C.

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