COMEDK2018MathematicsApplication of Derivatives

Let x be a number which exceeds its square by the greatest possible quantity, then x=

Options

A1 / 2
B1 / 4
C3 / 4
D1 / 3

Correct answer

A. 1 / 2

Step-by-step solution

Let the required numbers be x . Then, f(x)=x-x² f^ (x)=1-2 x For a local maxima or local minima, we must have aligned & f^ (x)=0 & 1-2 x=0 & 2 x=1 x= 1 2 aligned Now, f^ (x)=-2 < 0 So, x= 1 2 is point of local maxima. Hence, required numbers is 1 2 .

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