Boundary Min and Max
- Dr. Doug Davis, 3D
This is an illustration of why an open boundary cannot be a minimum or maximum value. The curve with a closed boundary at and an open boundary at . Approaching the closed boundary the value decreases until you get to the boundary point where . Therefore the boundary point is a minimum value. Approaching the open boundary, the value increases but when you reach the boundary point the value is undefined. For any point close to the open boundary there exist a point closer to the boundary with a greater value. Therefor you cannot define a point where the value is a maximum.
Move the orange plus symbol to move the value towards 1. Note how the value changes as you approach and get to . Left of 1 the value is undefined. Move the value towards 3. Note that when you get to the value is undefined so is not a maximum. In order to see points very close to check the AutoZoom checkbox. This will enlarge the scale as approaches 3. Note that within computer accuracy you do not reach a maximum value for . The curve continues upwards to the right of the point. ( If you get to close computer roundoff will cause the curve to not be shown. ) Note the coordinates of the top left corner and the bottom right corner of the graph to indicate the scale.