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

• Feb 1st 2011, 08:24 PM
elpermic
Where does the plane tangent to z = e^(x-y) at (1,1,1) meet the z axis?
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?
• Feb 1st 2011, 09:17 PM
TheEmptySet
Quote:

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 $(x,y)=(0,0)$