I'm having problems finding the extrema of the function $h(x, y) = 2x sin(y) + y^2−x^2$. There is supposed to be one saddle point but I can't seem to get that. I tried taking $f_{xx}f_{yy} - f_{xy}^2$, but I can't seem to end up with 0. Anyone knows how to solve this problem? Would really appreciate it!
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Did you calculate the gradient ? – Peter Jan 18 '15 at 19:31
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I found $h_x = 2siny - 2x$ and $h_y = 2xcosy + 2y$ – thbcm Jan 18 '15 at 19:42
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This is correct. They both must be $0$. So, $x=siny$ and $x=\frac{-y}{cos(y)}$ – Peter Jan 18 '15 at 20:16
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Did you check, if the origin is a saddle point ? – Peter Jan 18 '15 at 20:18