SinceOriginally Posted by fring
The minimum of , if it exists, occurs either at an end point of the valid interval for or at a stationary point of . A quick check shows the minimum does not occur at , so it must occur at a stationary point.
The stationary points of this occur when:
which simplifies to:
so either , or .
Now we need to classifty these stationary points. Examining the second derivative of at the relevant points shows that corresponds to a local minimum and that minimum is , and the other point corresponds to a local maximum. Comparison between all the maxima, and minima shows that these are all global maxima and minima, so: