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#### GreenGoblin

##### Member

- Feb 22, 2012

- 68

Please help me solve this problem and help me find if I made a mistake? If you will,

Thank you

$f(x,y) = 2cos(2x) + sin(x^{2}-y^{2})$

Find all the first and second order derivatives, hence show the origin is a critical point and find which type of critical point

First time attempting critical point question, I know it has to do with second derivative but I am not sure on what the definition is,

I made the derivatives (I don't have any way to verify this other that my own mind and it needs to be right to check the critical point criteria I figure, so please point out to me any mistake)

$df/dx = -4sin(2x) + 2xsin(x^{2})cos(y^{2}) - cos(x^{2})sin(y^{2})$

$df/dy = -2y(sin(y^{2})sin(x^{2}) + cos(y^{2})cos(x^{2}))$

$d^{2}f/dx^{2} = -8cos(2x) + 4x^{2}cos(x^{2})(sin(y^{2}) + cos(y^{2})) + 2sin(x^{2})(sin(y^{2}) + cos(y^{2}))$