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  • 5 years ago

Localate all critical points for the function z = x² - 4xy/(y²+1). Hence classify them as local maximum, local minimum or saddle points if exist

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  1. anonymous
    • 5 years ago
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    I don't have time to do this question, but here's how you do it say that function f is x² - 4xy/(y²+1) find derivative of that function with respect to x, call that fx then, with respect to y, call that fy set both equal to zero and solve for local mins and maxs. these are the critical points of the function then using the second derivative test, you can find local min and max find the derivative of fx with respect to x and y, calling them, fxx and fxy find the derivative of fy with respect to y, calling it, fyy apply second derivative test D = fxx(a,b) * fyy(a,b) - [fxy(a,b)]^2 (where (a,b) are the critical points that you've found) if D > 0 and fxx(a,b) is > 0, then f(a,b) is local min if D > 0 and fxx(a,b) is < 0, then f(a,b) is local max if D = 0 saddle point. good luck

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