Question

calculate the rest - maximum (file attached in second post)

Answer 1

are you asking if your steps are correct?

Answer 2

No, I'm asking who can calculate the maximum part for me. I'm not done yet, I should also find the maximum value

Answer 3

ok

Answer 4

there is no max,
as x and y approach infinity, f approaches infinity

Answer 5

but my teacher said i should also find the max

Answer 6

he said it wasn't correct, because i still need to find the maximum value

Answer 7

oh...ok
the question says \[x,y \in [0;2]\]

Answer 8

so we are looking for max and min only inside that interval

Answer 9

Can you help, because I'm really lost

Answer 10

you have established that (1, 1/4) is the local minimum,
so the maximum occur at the boundary points: either (0,0) and (2,2)

Answer 11

But how do I calculate the answer?

Answer 12

sorry, boundary points would be (0,0) (2,0) (2,2) (0,2)
..i'm not sure, but i guess you will have to evaluate 'f' at each of these points

@Kainui

Answer 13

Okay :) Anyone who can calculate the answer?

Answer 14

@IrishBoy123

Answer 15

after (1, 1/4) \(f_x , f_y\) both increase with increase in x and y, so i would go with (2,2) as the max points

substitute x=y=2 to evaluate f

Answer 16

ok...now i'm thinking we should consider the points farthest from (1/4, 1)
so that would be (2,0) and (2,2)

Answer 17

@ganeshie8

Answer 18

yeah the extrema can occur at boundary too
http://www.wolframalpha.com/input/?i=max+x%5E2-x%2F2%2By%5E2%2F4-5-y%2F2%2C+0%3C%3Dx%3C%3D2%2C+0%3C%3Dy%3C%3D2%2C+

Answer 19

thanks!!

Answer 20

Someone who can explain how the calculations should be written? :)

Answer 21

@Lillery maxima occur at (2,0) and (2,2)
f evaluates to -2 at both points

Answer 22

write this:
we test points (2,0) and (2,2) as they are points that are furthest from the minima in the given domain,

f=-2 at both (2,0) and (2,2)
therefore both these points are the maxima

Answer 23

Thank you!!!