Question

Find absolute max and min of the function on the given domains

Answer 1

F(x,y)=48xy-32x^3-24y^2 on the rectangular plate
0 less than or equal to x less than or equal to 1,
0 less than or equal to y less than or equal to 1

Answer 2

find the partials, set them equal to 0 and solve for critical points

Answer 3

(work so far)
\[f_{x} = 48y-96x^{2} , f_{y}=48x-48y\]
\[48(y-2x^{2})=0 , 48(x-y)=0\]

Answer 4

Yes

Answer 5

I got x = 0 & x=1/2

Answer 6

from there I'm not quite sure what to do

Answer 7

would my critical points be (0,0) (1/2,1/2), (0,1/2), (1/2,0) ???

Answer 8

looks good

Answer 9

Hm ok! @rational are the critical points I listed correct?

Answer 10

Yes, familair with second derivative test ?

Answer 11

somewhat! we just recently began covering this material and its a little confusing