1. Organize the following into 2 categories: DERIVATIVES & INTEGRALS Slope of a Tangent Line Slope of a Curve Instantaneous Rate of Change Find where a function is increasing Find where a function is concave down Find an inflection point Find a critical point Finding a maximum of a function Finding a Rate of Change Chain Rule Product Rule Given a Rate, Find a Total Area under a curve Area between Curves Volume of a Solid U-Substitution Given Acceleration, Find Distance Given Velocity, Find Displacement Riemann Sums Anti-Derivative

2. Calculus BC Unit 1 Day 1 Little Review Where have we been Where are we going

3. Where Have We Been Calc AB Break Down 1)Limits 2)Derivatives 3)Applications of Derivatives 4)Integrals 5)Application of Integrals

4. Limits Graphically

5. Limits Algebraically Methods: 1)Plug in 2)Factor 3)Getting Sneaky (Multiplying by “1”) 4)Some you just have to remember

6. Big Point of Limits: Continuity

7. Derivatives!!! Ready?!?! Names: Slope of a Tangent Line Slope of the Curve Instantaneous Rate of Change

8. Examples of Derivatives we’ve Learned

9. What the Derivatives tells us!

10. Applications of Derivatives 1)Equation of Tangent Line 2)Equation of Normal Line (perpendicular) 3)Finding Max & Minimums 4)Related Rates Problems 5)PVA We will do examples of these as warm ups over the next couple of days!

11. Integrals Integrals are Anti-Derivatives!

12. Applications of Integrals 1)Area between curve and x-axis 2)Area between 2 curves 3)Volumes of Solids 4)Integrating a Rate to find a Total 5)Average Value of a Function (Actually didn’t cover… woops! We will though!) We will do examples of these as warm ups over the next couple of days!

13. Integration methods 1)U-Substitution  Reverse Chain Rule 1)Integration By Parts  Reverse Product Rule

14. U-Sub Practice (Hint – Find the insides) 1) 2) 3)

15. Integration by Parts – 2 Functions being multiplied! GivenFind Steps: 1)Label f(x) and g’(x) 2)Find their counterpart 3)Plug in and Evaluate the Integral

16. Hardest Part: Labeling f(x) Here is a HINT!  This is NEW!!!! Pick f(x) by L. I. A. T. E.

17. Examples

18. Coming Up! Calculus BC Fancy Functions Unit 1: Polar Unit 2: Parametric & Vector Unit 3: More Applications of Integrals Series Unit 4: Infinite Series Unit 5: Power and Taylor Series