Consider the function \[f(x)={{e}^{-2x}}\]sin 2x over the interval \[\left( 0,\frac{\pi }{2} \right)\]. A real number \[c\in \left( 0,\frac{\pi }{2} \right)\,,\] as guaranteed by Rolle?s theorem, such that \[{f}'\,(c)=0\] is [AMU 1999]

Consider the function \[f(x)={{e}^{-2x}}\]sin 2x over the interval \[\

1.	Consider the function \[f(x)={{e}^{-2x}}\]sin 2x over the interval \[\left( 0,\frac{\pi }{2} \right)\]. A real number \[c\in \left( 0,\frac{\pi }{2} \right)\,,\] as guaranteed by Rolle?s theorem, such that \[{f}'\,(c)=0\] is [AMU 1999]
A.	\[\pi /8\]
B.	\[\pi /6\]
C.	\[\pi /4\]
D.	\[\pi /3\]
Answer» B. \[\pi /6\]

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Consider the function \[f(x)={{e}^{-2x}}\]sin 2x over the interval \[\left( 0,\frac{\pi }{2} \right)\]. A real number \[c\in \left( 0,\frac{\pi }{2} \right)\,,\] as guaranteed by Rolle?s theorem, such that \[{f}'\,(c)=0\] is [AMU 1999]

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