Question

Find absolute extrema on closed regions (using the u’s)

Determine absolute extrema of the given function over the closed region R:

f(x,y) = 4xy - y^2 - x

Where R is the region bounded by: x = 0, y = x, x + y = 6

Answer 1

@IrishBoy123

Answer 2

go for it

what are \(f_x \) and \(f_y \)?!?!

Answer 3

and have you sketched the region....?!?!

Answer 4

yes

Answer 5

Have you found the partial derivatives of the function?

Answer 6

@pooja195

@IrishBoy123

@Mehek14

Answer 7

that is my work

Answer 8

@IrishBoy123

Answer 9

i can look at it

Answer 10

yes that would be great :)

Answer 11

@geerky42

Answer 12

@freckles

Answer 13

@Hero

Answer 14

looks fine to me, i can see where you get the points from but all the real math seems to be missing. for example, the saddle point at \((\frac{1}{8}, \frac{1}{4})\), i think we can get higher deriv's and rule it out as a local max/min.

maybe you just wanted the numbers checked.... :p

[i have looked at the algebra only cursorily]

Answer 15

@blackstreet23

just noticed the earlier scans are different, so i guess that it is all there 😃

PS: tried my best to get a plot of this for a reality check and failed. but looks good to me. FWIW.

Answer 16

ohh btw I noticed that the point (3.5, 2.5) does not lie within the area, so that is not my max :/

Answer 17

but after that is everything else correct?

Answer 18

@pooja195

@Hero

@IrishBoy123

Answer 19

seems fine to me

Answer 20

Hi :)
@blackstreet23 It looks like @irishboy123 helped you already!

Answer 21

so is everything totally fine? like 100% sure. My professor is super picky!

Answer 22

this is for a takehome test

Answer 23

Everything looks fine.

Answer 24

^to me.

Answer 25

ohh ok. I will post my second question. Then. Thanks :)

Answer 26

:)

Answer 27

Thanks for helping @Iirishboy123 , greatly appreciated :D