Conditional maximum/minimum of a function

This applet enables you to visually inspect the behavior of a function of two variables above a curve in the xy-plane (rather than above a region in the plane). The thick reddish curve on the graph of f represents the set of points (x , g(x), f(x, g(x)) where y = g(x) is the said curve in the xy-plane.
Enter your function in the edit field to see its graph. You can use the provided parameters: a, b, c, h in your input, and then change their values with sliders.