A) \[-1\]
B) \[0\]
C) \[\frac{1}{2}\]
D) \[1\]
Correct Answer: C
Solution :
Let the number be \[x\], then\[y=x-{{x}^{2}}\] On differentiating w.r.t. x, on both sides, we get \[\frac{dy}{dx}=1-2x\] For greatest or least number, put\[\frac{dy}{dx}=0\] \[\therefore \] \[1-2x=0\Rightarrow x=\frac{1}{2}\] Again, differentiating, we get \[\frac{{{d}^{2}}y}{d{{x}^{2}}}=-2\]which is greatest \[\therefore \] Greatest number is\[\frac{1}{2}\].
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