f(x,y)=1/3*x^3 - 1/4x + y^2
Using Lagrenge Multiplier method on boundary, find the absolute maximum and minumum values of f(x,y).

D={(x,y) R^2 : (x-1)^2 + 4y^2

Question

f(x,y)=1/3*x^3  -  1/4x + y^2 
Using Lagrenge Multiplier method on boundary, find the absolute maximum and minumum values of f(x,y).

D={(x,y) R^2 : (x-1)^2  + 4y^2  <= 0 }

anonymous · Answer

are you sure that our constraint is equal to 0?

anonymous · Answer

sorry that is nat 0 it it is 4 

D={(x,y) R^2 : (x-1)^2 + 4y^2 <= 4 }

anonymous · Answer

ah there we go,

okay there are two cases that we must consider here,


first is that you need to solve for the max and min values using this constraint:

$$(x-1)^2+4y^2=4$$

anonymous · Answer

Then the second case , is that you need to find the max and min using this constraint:

$$(x-1)^2+4y^2<4$$

anonymous · Answer

or we can write the constraint as:|dw:1337005779847:dw|