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Calculus and Beyond Homework Help
Using an ODE to show a local minimum
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[QUOTE="ver_mathstats, post: 6447911, member: 650531"] [B]Homework Statement:[/B] Using the ODE, show that the solution has a local minimum at x = 0. [B]Relevant Equations:[/B] First derivative test The ODE given to us is y' = xcosy. I am having a bit of trouble when it comes to solving this problem. We are supposed to show that the solution has a local minimum at x = 0 with the hint to think of the first derivative test. However, I am only really familiar with the first derivative test when it comes to a function like f(x) not y' with two variables. In order to solve this would be have to first take f(x,y) = xcosy and then solve the partial derivatives f[SUB]x[/SUB](x,y) and f[SUB]y[/SUB](x,y), then equate them both to zero, solve for x and y to obtain a critical point, and finally calculate the second partial derivatives to prove there is a local minimum at x = 0? Or is there a much more efficient way to do this? Any help would be appreciated as I'm a bit confused about how to approach this, thank you. [/QUOTE]
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Using an ODE to show a local minimum
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