Where does the plane tangent to z = e^(x-y) at (1,1,1) meet the z axis?

**elpermic** · February 1st 2011, 07:24 PM

Where does the plane tangent to z = e^(x-y) at (1,1,1) meet the z axis?

How do I go about solving this problem? Am I suppose to use the tangent plane equation?

**TheEmptySet** · February 1st 2011, 08:17 PM

Originally Posted by elpermic

Where does the plane tangent to z = e^(x-y) at (1,1,1) meet the z axis?

How do I go about solving this problem? Am I suppose to use the tangent plane equation?

The equation of the tangent plane is going to be

$\displaystyle z=z_0+\frac{\partial z}{\partial x}\bigg|_{(x_0,y_0)}(x-x_0)+\frac{\partial z}{\partial y}\bigg|_{(x_0,y_0)}(y-y_0)$

This plane will meet the z-axis when $(x,y)=(0,0)$

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