A) \[-1/4\]
B) \[-1/3\]
C) \[1/6\]
D) \[1/5\]
Correct Answer: C
Solution :
\[f(x)=\frac{x}{4+x+{{x}^{2}}}\] Differentiate, \[{f}'(x)=\frac{4+x+{{x}^{2}}-x(1+2x)}{{{(4+x+{{x}^{2}})}^{2}}}\] For maximum \[f'(x)=0\] Þ \[\frac{4-{{x}^{2}}}{{{(4+x+{{x}^{2}})}^{2}}}=0\] Þ \[x=2,\,-2\] Both values of x are out of interval \ \[f(-1)=\frac{-1}{4-1+1}=\frac{-1}{4}\], \[f(1)=\frac{1}{4+1+1}=\frac{1}{6}\] (maximum).You need to login to perform this action.
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