1. AP Calculus Chapter 2, Section 1 THE DERIVATIVE AND THE TANGENT LINE PROBLEM 2013 – 2014 UPDATED 2015 - 2016

2. The Tangent Line Problem Calculus grew out of four major problems that European mathematicians were working on during the seventeenth century. 1.The tangent line problem 2.The velocity and acceleration problem 3.The minimum and maximum problem 4.The area problem Isaac Newton (1642 – 1727) is the first to get credit for giving the first general solution to the tangent line problem.

3. What does it mean to say a line is tangent to a curve at a point?

4. Slope of the tangent line

5. Definition of Tangent Line with Slope m

6. Translation:

7. Derivative Notation

14. Using the previous derivative, discuss the behavior of f at (0, 0)

17. A graph with a sharp turn

18. Differentiability and Continuity If a function is differentiable at x = c, then it is continuous at x = c. So differentiability implies continuity. It is possible for a function to be continuous at x = c and not be differentiable at x = c. So, continuity does not imply differentiability.

19. Vertical Tangent Lines

21. Ch. 2.1 Homework Pg. 104 – 106: #’s 7, 11, 17, 23, 27, 57, 63, 81