We said earlier in the section that it is not good enough to say local extrema exist where a function changes from increasing to decreasing or vice versa. Consider the four functions (Function I, II, III, IV) graphed below. Notice that all four of them change direction at an open circle on the graph. Examine each for local extrema. What is the effect of placing the ``dot'' on the y-axis above or below the open circle? What could you say if no function value were assigned to x=0?
((a)) Function I
((b)) Function II
((c)) Function III
((d)) Function IV