How do I find the critical point for f(x,y)=xy-e^x?

SuperHead

From: US
Posts: 14
Votes: 28
I got the partial derivatives df/dx=y-e^x and df/dy=x-e^x, but i do not know how to solve for any of the variables...

 

Answer No.1

Anonymous

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Given: f(x, y) = x*y - exp(x) The critical point exists at a set of values of x and y where both partial derivatives equal zero. df/dx = 0 df/dy = 0 Thus: y - exp(x) = 0 x - exp(x) = 0 Unfortunately, there is no solution in terms of elementary functions. This is an ugly one, where we are stuck with a non-analytic solution. My Computer Algebra Software recommends that x=-LambertW(-1). I've never even heard of Lambert functions in my life. Even more unfortunate, there is no real number solution to x = exp(x). Plot a simple graph of both functions, and you will see no ordinary intersection. Conclusion: there isn't any critical point for this particular function, if you are limited to the real number domain of x and y. Nicely put, Many thanks! buy cialis us pharmacy cialis without a doctor prescription can i buy cialis over the counter in hong kong buy cialis online

Answer No.2

Anonymous

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