MATH 1300 Study Guide - Final Guide: Differential Calculus, Misleading Graph, Constant Function

• School: York University
• Department: Mathematics and Statistics
• Course: MATH 1300
• Professor: Shu Xiao Li

Document Summary

Section 1: the mean value theorem: we will see that many of the results depend on one central fact, which is called the. Theorem, in the form given by equation, says that there is at least one point psc, f scdd on the graph where the slope of the tangent line is the same as the slope of the secant line ab. In other words, there is a point p where the tangent line is parallel to the secant line ab. Example: let"s apply rolle"s theorem to the position function s f std of a moving object. 9scd 0; that is, the velocity is 0. In particular, you can see that this is true when a ball is thrown directly upward. But: since for all x, so f 9sxd can never be 0, this gives a contradiction, therefore the equation can"t have two real roots.