## Tangent plane

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A tangent plane to a function $$f(x,y)$$ at a point $$P (x_0,y_0)$$ is the plane which contains all tangent lines along all traces through $$P$$. The following diagram illustrates this idea.

We say that $$f(x,y)$$ is differentiable at $$P(x_0,y_0)$$ if such a plane exists at $$P$$. In this case we can find the plane by using only the trajectories parallel to the $$xz$$-plane and the $$yz$$-plane.

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1. Make sure you have the latest version of Java 7 installed in your computer. Tablets and smartphones are not supported.