In this lecture we are going to talk about Mean Value Theorem and Rolles Theorem. We are going to introduce both of these theorems and see their graphical explanations. The mean value theorem states, roughly: that given a planar arc between two endpoints, there is at least one point at which the tangent to the arc is parallel to the secant through its endpoints. Rolle's theorem essentially states that any real-valued differentiable function that attains equal values at two distinct points must have a stationary point somewhere between them - that is, a point where the first derivative is zero. We will see that Rolles Theorem is simply a special case of the Mean Value Theorem.
*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.
First Derivative Test, Second Derivative Test
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.