- #1

arl146

- 343

- 1

## Homework Statement

Use Lagange Multipliers to find the max and min values of the function subject to the given constraint(s). f(x,y)=exp(xy) ; constraint: x^3 + y^3 = 16

## Homework Equations

[itex]\nabla[/itex]f = [itex]\nabla[/itex]g * [itex]\lambda[/itex]

f

_{x}= g

_{x}* [itex]\lambda[/itex]

f

_{y}= g

_{y}* [itex]\lambda[/itex]

## The Attempt at a Solution

Set the fx and fy eqns equal to 0. but i can't solve for x, y, and lambda... i guess my algebra isn't that strong

i got f

_{x}= [itex]\lambda[/itex] * g

_{x}

y*e

^{xy}= 3x

^{2}[itex]\lambda[/itex]

and for y:

x*e

^{xy}= 3y

^{2}[itex]\lambda[/itex]

and g(x,y) = x

^{3}+ y

^{3}= 16