A) \[x=0\]
B) \[x=-1\]
C) \[x=-n\]
D) \[x=n\]
Correct Answer: C
Solution :
\[f(x)=x{{e}^{x}}\] \[{f}'(x)={{e}^{x}}+x{{e}^{x}}\] \[{f}''(x)={{e}^{x}}+{{e}^{x}}+x{{e}^{x}}=2{{e}^{x}}+x{{e}^{x}}\] \[{f}'''(x)=2{{e}^{x}}+{{e}^{x}}+x{{e}^{x}}=3{{e}^{x}}+x{{e}^{x}}\] ????????????????? ????????????????? \[{{f}^{n}}(x)=n{{e}^{x}}+x{{e}^{x}}\]. Now, \[{{f}^{n}}(x)=0\] Þ \[n{{e}^{x}}+x{{e}^{x}}=0\] Þ\[x=-n\].
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