Question

4. Find the maximum value of e^2xy given the constraint x^2+y^2=4 . Assume that x and y are positive.

Answer 1

Can anyone help me?

Answer 2

\[x = \sqrt{ 4 - y^2}\]
\[z = e^{2xy} = e^{2y \sqrt{4-y^2}}\]

now differentiate w/ respect to y and set = 0

Answer 3

I have Fx=e^2xy-2x(lamda-don't know how to type that here.)
Fy=e^2xy-2y(lambda)
Cannot figure out F(lamda)...

Answer 4

\[ dz/dy =(2\sqrt{4-y^2} -2y\frac{y}{\sqrt{4-y^2}})e^{2y \sqrt{4 - y^2}}=0\]

Answer 5

f(x,y)=e^2xy
g(x,y)=x^2+y^2-4
F(x,y,lamda)=f(x,y)-lamda*g(x,y)
Does any of this make sense?

Fx=e^2xy-2x(lamda-don't know how to type that here.)
Fy=e^2xy-2y(lambda)
Cannot figure out F(lamda)...

Answer 6

\[2\sqrt{4-y^2} -2y\frac{y}{\sqrt{4-y^2}} =0\]

\[4 - y^2 = y^2\]

\[y = \sqrt2\]

Answer 7

does that make sense?

Answer 8

im not 100% its an educated guess

Answer 9

No. but thank you! :)

Answer 10

if y^2 + x^2 = 4

then x = sqrt(4 - y^2)

substitute this into f(x,y)

to get an explicit function f(y)

then differentiate

Answer 11

*a one variable function