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If fx=-1.3 and fy= 2.6 is fxy positive or negative? I'm thinking that since fy is positive and greater then fx (who is negative) it will be positive?

I estimated fx and fy from a contour plot. On the contour plot the f(x,y) is more curves then lines. So maybe fx = -1.3x and fy= 2.6y ? Thanks for help!enter image description here

John
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    If the partial derivatives $f_x$ and $f_y$ are constant, the function has shape $ax+by+c$, and $f_{xy}$ is identically $0$. If the partials are $-1.3$ and $2.6$ at a particular point, we can say nothing about $f_{xy}$ at that point. – André Nicolas Oct 10 '13 at 19:05

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If the partial derivatives $f_x$ and $f_y$ are constant, the function has shape $ax+by+c$, and $f_{xy}$ is identically $0$.

If the partial derivatives are $-1.3$ and $2.6$ at a particular point, we can say nothing about $f_{xy}$ at that point.

Examples: Let $f(x,y)=-1.3x+2.6y+88xy$. Then $f_x(0,0)=-1.3$, $f_y(0,0)=2.6$, and $f_{xy}(0,0)=88$, positive.

Using $f(x,y)=-1.3x+2.6y-88xy$, we get the same first partials at $(0,0)$, but $f_{xy}(0,0)=-88$, negative.

Using $f(x,y)=-1.3x+2.6y-x^2y$, we get the same first partials at $(0,0)$, but $f_{xy}(0,0)=0$.

André Nicolas
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  • Added the plot now, I don't understand how I'm going to find out about fxy. Could you say that since the distance between the curves are increasing alot when x and y get bigger that fxy will be negative? – John Oct 11 '13 at 01:15