Drag the point [math]\left(a,g\left(a\right)\right)[/math] along the graph by moving the slider. Observe how the values of g(a), g'(a), and g''(a) change. Here are some questions you can ask: [br][br]- What is the graph doing when g'(a) is positive? Negative? Zero? [br]- What is the graph doing when g''(a) is positive? Negative? Zero?[br]- Are there points where all three values are positive? What about just two? What about one? Or none?