(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

2. Relevant 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]

3. The attempt at a solution

Set the fx and fy eqns equal to 0. but i cant solve for x, y, and lambda... i guess my algebra isnt 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

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# Lagrange Multipliers to find max/min values

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