The average value of a function on a surface is the sum of all the values of the function over the surface, divided by the total surface area. This value represents the "center of mass" of the function on the surface.
The formula for finding the average value of a function on a surface is:
average value = (integral of function over surface) / (surface area)
Yes, the average value of a function on a surface can be negative. This means that the values of the function are mostly below the surface and the center of mass is below the surface.
The average value of a function on a surface is the same as the average value of the function on a line if the surface is a flat plane. However, if the surface is curved, the average value on a line may be different from the average value on the surface.
Yes, the average value of a function on a surface can change if the surface is rotated or translated. This is because the surface area and the values of the function over the surface will change, resulting in a different average value.