Explore Critical Points/Numbers

Critical points (numbers) are useful in studying local extrema and increasing decreasing behavior of a function. A point in the domain of a function is said to be a critical point of if either derivative of does not exist at or the derivative of at is . Use this GeoGebra applet to explore critical points. Input a function in the box. Set the left endpoint of the interval using slider a and right endpoint using slider b, so that domain of definition of is . Now use slider c to explore critical points. If a critical point is rightly spotted a reinforcement [You Did It] appears. As help you may check one or both of Show Derivative value and Show Tangent check boxes. For more on behavior of functions check my online book "Flipped Classroom Calculus of Single Variable" https://versal.com/learn/vh45au/