Estimate the limit by graphing the function for an appropriate domain. Confirm your estimate by using L'Hopital's rule.
Show each step of your calculation.
-Given that $x 0$, find the maximum value, if any, of $x ^ { 1 / x ^ { 6 } }$.
A) $e ^ { 6 e }$
B) $\mathrm { e } ^ { 1 / ( 6 \mathrm { e } ) }$
C) 1
D) $\infty$

Question

Estimate the limit by graphing the function for an appropriate domain. Confirm your estimate by using L'Hopital's rule.
Show each step of your calculation.
-Given that $x > 0$, find the maximum value, if any, of $x ^ { 1 / x ^ { 6 } }$.
A) $e ^ { 6 e }$
B) $\mathrm { e } ^ { 1 / ( 6 \mathrm { e } ) }$
C) 1
D) $\infty$

Quizplus · Accepted Answer

The maximum value of $x ^ { 1 / x ^ { 6 } }$ occurs when $x = e ^ { 1 / ( 6 e ) }$.

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