Another Optimization problem...
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leading to Snell's Law
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1.  

<A HREF="https://people.ucsc.edu/~rmont/classes/ClassicalGeometry/web2017/lectures/SnellHere/SnellProb1.pdf"> The lifeguard's conundrum </A>

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2.  Set-up of the optimization problem.

a) choose names for variables

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b) set up the constraint (or pre-choose variables well )

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c) write the function to be minimized in terms of the constraint

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2. Minimize, by setting the derivative of the function to zero.

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3.  Reality check your solution--- where is the guard crossing vs where you expect them to.

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 More on Snell, Fermat, .. etc : 
 
 <A HREF="https://people.ucsc.edu/~rmont/classes/ClassicalGeometry/web2017/lectures/SnellHere/"> here </A>