# Function of Two Variables

## Description

Below is an interactive illustration of a function of x and y. The z axis is the value of the function. The point, , can be moved with the sliders which change the and values of the point. Dashed lines on the surface show the functions values along constant or values. There are several check boxes that allow you to show various parameters of the function at the point .
• Normal Line - shows a line perpendicular to the surface
• Tangent Plane - shows a plane that is tangent to the surface. Any line in this plane through will also be tangent to the surface.
• Tangent Line (x=xA) - shows a line in a constant plane that is tangent to the surface. The plane is also shown lightly.
• Tangent Line (y=yA) - shows a line in a constant plane that is tangent to the surface
• Gradient Vector - shows the gradient vector which is in an plane and points in the direction of increasing function value
• Contour Line - shows a contour curve where the function value is constant
Moving the view around is a good way to see the three dimensional features. Try viewing the the gradient and contour line from directly above the surface. Notice the angle between the vector and the curve. Equations for all of the items are shown when the box is checked.