1. { Semester Exam Review AP Calculus

2. Exam Topics

3. Trig function derivatives

4. Differentiate: Co-Functions: Negative!!

5. Find f’(x) using the limit definition of derivatives:

6. Derivatives by limits:

7. Rate of Change: Average vs. Instantaneous

8. DERIVATIVE!!!! (Slope of tangent line) Instantaneous Rate of Change =

9. Writing Equation of Tangent Line

10. Displacement/Velocity/Acceleration

11. Implicit Differentiation:

12. Differentiate implicitly:

13. To the nearest thousandth, calculate the slope of the tangent where x = 4:

14. Differentiate implicitly:Find coordinates of y when x = 4 and substitute into dy/dx equation:

15. Useful Related Rates Formulas

16. Be able to find values that make a piecewise function differentiable at a given point (must be continuous AND differentiable) Remember to use LIMITS to show differentiability and continuity! Differentiability Implies Continuity

17. To Prove Continuity:

18. Trapezoidal Rule/Riemann Sums

19.  Implicit Differentiation  Differential dy  Average Rate of Change  Instantaneous Rate of Change  Estimate definite integrals using trap rule, Riemann sums, graph  Applications  Find velocity given displacement equation  Find displacement given velocity equation  Write equation of tangent line  Find c value guaranteed by Mean Value Theorem  Related Rates  Calculator  Find numerical derivatives  Table of Values/Graph  Riemann Sums/Trapezoidal Rule Program (especially for large values of n!) Exam Topics Checklist