On Sun, 6 Apr 2008 22:04:20 -0400, "Greg Neill"
<gneillREM@[EMAIL PROTECTED]
> wrote:
>"Barry Schwarz" <schwarzb@[EMAIL PROTECTED]
> wrote in message
>news:6iriv391mktkqhluj62j67e7ehf6b66ms6@[EMAIL PROTECTED]
>
>>
>> The total time is obviously the sum of the two times above. What is
>> the standard method for determining where a function has a local
>> minimum?
>
>Differentiate the function with respect to the
>variable to be minimized and set the resulting
>expression to zero. Solve for the variable in
>question. That will yield maxima, minima, or
>both (if there are multiple roots). Technically,
>they are called inflection points. Check each
>solution to determine what it is, or apply the
>"second derivative test".
To the OP:
Additionally, don't forget the variable x lies on the closed interval
[0,150], leaving the possibilities that the lifeguard swim directly to
the swimmer or run to the closest point on the beach to the swimmer
before swimming. Depending on the relative rates and distances, either
end point might be where the minimum time happens. Check them.
--Lynn
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