I know that a tangent plane is given by:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]a(x-x_0)+b(y-y_0)+c(z-z_0)=0[/tex]

Where <a,b,c> is the gradient vector. When I was given the problem of writing an equation (z=...) for it, I replaced <a,b,c> with the partials that compose the gradient vector:

[tex]\left<a,b,c\right >=\left<\frac{\partial f}{\partial x},\frac{\partial f}{\partial y},\frac{\partial f}{\partial z}\right >[/tex]

Now I have:

[tex]\frac{\partial f}{\partial x}(x-x_0)+\frac{\partial f}{\partial y}(y-y_0)+\frac{\partial f}{\partial z}(z-z_0)=0[/tex]

This is where I am having trouble solving for z because of the partial in front of it.

Any suggestions?

Thanks a lot.

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# Equation of a Tangent Plane

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