In this demo, we show some slices of the tangent hyperplane at a point P on a function graph of three variables.

We slice the tangent plane in the direction of the coordinate axes at the hotspot P (in blue), which you can move around in the Domain-Window. In the Slices-Window you can see the colored slice surfaces of the function graph at the point . As usual, the color of the slice corresponds to the value of f(x,y,z).

The slice surfaces are then displayed as function graphs in the XY-, YZ- and XZ- Slices Windows, together with the slices of the tangent hyperplane. Note that the slices of the tangent hyperplane are the tangent planes of the slices(Why?).