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## Homework Statement:

- Ann is in point ##(2,0)## and walks to KFC in ##(-2,0)##.On her way there’s a pond within the curve ##\big|x \big|+\big|y \big|=1##.She walks 5 km/h outside the pond and ##\frac{5\sqrt{5}}{2\sqrt{2}}## km/h in the pond. In which point does she enter the pond, or should she walk around?

## Relevant Equations:

- The derivative.

Ok. So if i sketch the curve I can see that this pound has a shape of a square. Ann and KFC has the same distance from the pond. I'm able to calculate the time for Ann to walk around the pond, and if she walks in a straight line from where she stands to KFC.

If she walks around it will take about 0,96 hours and if she walks in straight line (enter pond in 1,0), it will take her 0,90. I did this using some simple geometry. But I don't know if Ann should rather enter the pond somewhere else to save time. So this must be an extreme value problem where I should make some sort of a function and find the derivative. I might be wrong about this, but that's the only assumption I have for now. How do I make such a function?

If she walks around it will take about 0,96 hours and if she walks in straight line (enter pond in 1,0), it will take her 0,90. I did this using some simple geometry. But I don't know if Ann should rather enter the pond somewhere else to save time. So this must be an extreme value problem where I should make some sort of a function and find the derivative. I might be wrong about this, but that's the only assumption I have for now. How do I make such a function?