SOLUTION: Hi! Find the local maximum and minimum values of the function and the value of x at which each occurs. State each answer correct to two decimal places. g(x)=1/4x^x (x>0) t

Algebra ->  Functions -> SOLUTION: Hi! Find the local maximum and minimum values of the function and the value of x at which each occurs. State each answer correct to two decimal places. g(x)=1/4x^x (x>0) t      Log On


   

Question 198715: Hi!
Find the local maximum and minimum values of the function and the value of x at which each occurs. State each answer correct to two decimal places.
g(x)=1/4x^x (x>0)
thanks for your help!
Answer by solver91311(24713) About Me  (Show Source):
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Obtain the first derivitive:

First take the natural log of both sides:



Differentiate with the chain rule on the left and the product rule on the right:






Set the first derivative equal to zero:



Since ,

if and only if



Hence



Therefore is a local extreme point.

The calculator tells us that but , and , so we can be assured that this is a minimum.





John