A) \[\frac{24}{25}\]
B) \[\frac{18}{25}\]
C) \[\frac{4}{5}\]
D) \[\frac{6}{25}\]
Correct Answer: A
Solution :
Differentiability we get \[f(x)=2x-{{x}^{2}}f(x)\] |
\[f(x)=\frac{2x}{1+{{x}^{2}}}\Rightarrow f''(x)=2\frac{(1-{{x}^{2}})}{{{(1+{{x}^{2}})}^{2}}}\] |
\[f'\left( \frac{1}{2} \right)=\frac{24}{25}\] |
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