A small island is 4 miles from the nearest point P on the straight shoreline of a large lake. If a woman on the island can row a boat 3 miles per hour and can walk 4 miles per hour, where should the boat be landed in order to arrive at a town 11 miles down the shore from P in the least time?
She must row a distance of :
She must walk a distance of :
The time traveled over water plus the time traveled over land can be written:
If this is correct, how would I find the derivative of the above function..?
Would this be the derivative?
Finding a common denomenator:
?
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I figured out the solution myself. If anyone is curious to how I solved it, here is what I did:
From here I plugged in 0, 11, and back into my original equation. I found that was the minimum time that occured at the stationary point. Therefore, she would land the boat miles down the shore from point P.