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In the following exercises, solve the given maximum and minimum problems.Ship $A$ is traveling due east at $18.0 \mathrm{km} / \mathrm{h}$ as it passes a point $40.0 \mathrm{km}$ due south of ship $B$, which is traveling due south at $16.0 \mathrm{km} / \mathrm{h}$. See Fig. $24.58 .$ How much later are the ships nearest each other?

Calculus 1 / AB

Chapter 24

Applications of the Derivative

Section 7

Applied Maximum and Minimum Problems

Derivatives

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Harvey Mudd College

Baylor University

Lectures

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Cruise Ship Travel At noon…

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At noon, ship $ A $ is $ 1…

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Solve each problem. When a…

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Boats A and B leave the sa…

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a cruise ship here given ECN on the cruise ship celebration is 60 miles due to south off the cruise ship inspiration. And now I'm going toe show you the figure. So now this you just think it at? No, the cruise ship celebration This is the celebration. Crucitti is at 60 mile didn't salt off the cruise ship inspiration. And now and it's silly at rate of 30 MPH. So this is the spirit 30 MPH and then the inspiration is selling west at a rate of 20 miles. So this is a 20 MPH. So at that blinked here, this is a distance. The point here I can I didn't speak. So not because invest. And then the s comes to UPI. Now we have to find the minimum distance. What is the minimum distance between them? So for this also, we know that initially the detect 60 miles So this point is yeah, this point is 60 miles from the going to be So now this is the distance city and now this will be 60 minus 30 x Now this will do. The 61 are 30 x and now this will with simply 20 x. So now this was with a plus 20 x. So now this is 20 X now a square board better and then take route. And now we have to find the minimum value. So now we have to solve it. So now then can be taken as common. So this will be six minus three X toe Holy square plus two x two Holy square. And now this would be also deserve diesel. So this will with 36 plus nine excess square minus dissolute 36 X Right now this would with four Xs query questions, you know? So this will be 30 13 x squared minus 36 then this will with the bluster genetics. So by soldering, we get X equals Toe Citizen with 33.28 miles and now we have to find the time. So on our putting these values on the question that the Texas called ability we've obtained by the combination of these two inspiration and celebration. So now we got 1.38 are so that wins at he had after 1.38 ours. This will wither at the minimum distance between the inspiration and deliberation

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