This is an illustration of why an open boundary cannot be a minimum or maximum value. The curve [math]f\left(x\right)=x^2,\text{ for }1\le x<3[/math] with a closed boundary at [math]x=1[/math] and an open boundary at [math]x=3[/math]. [br][br]Approaching the closed boundary the [math]y[/math] value decreases until you get to the boundary point where [math]y=1[/math]. Therefore the boundary point is a minimum value.[br][br]Approaching the open boundary, the [math]y[/math] value increases but when you reach the boundary point the [math]y[/math] value is undefined. For any point close to the open boundary there exist a point closer to the boundary with a greater [math]y[/math] value. Therefor you cannot define a point where the [math]y[/math] value is a maximum.

Move the orange plus symbol to move the [math]x[/math] value towards 1. Note how the [math]y=f(x)[/math] value changes as you approach and get to [math]x=1[/math]. Left of 1 the [math]y[/math] value is undefined. [br][br]Move the [math]x[/math] value towards 3. Note that when you get to [math]x=3[/math] the [math]y[/math] value is undefined so [math]f(3)[/math] is not a maximum. In order to see points very close to [math]x=3[/math] check the AutoZoom checkbox. This will enlarge the scale as [math]x[/math] approaches 3. Note that within computer accuracy you do not reach a maximum value for [math]y[/math]. 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.