1. Warm Ups

2. AP Calculus 3.1 Tangent Line Problem Objective: Use the definition to find the slope of a tangent line

3. History Calculus grew out of 4 major problems Tangent Line Problem Fermat (1601 – 1665) Descartes (1596 – 1650) Huygens (1629 – 1695) Barrow (1630 – 1677) Newton (1642-1727) Leibniz (1646-1716)

4. Slope of a Secant line

5. Slope of a tangent line

6. Example

7. Definition of a derivative

8. Find the derivative of… f(x) = x 3 + x 2 f’(x) =

9. Find the equation of a line Find the equation of the line tangent to the function f(x) = x 2 + 2x + 1 at the point (-3, 4).

10. Differentiability A function is not differentiable at c if the function is not continuous at c f(x) = [x] the limits are not the same on both sides of c (sharp point) f(x) = |x| tangent line is vertical at c f(x) = x 1/3

11. Assignment Page 1245 – 33 eoo, 37 – 40, 57