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{ Semester Exam Review AP Calculus. Exam Topics Trig function derivatives.

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Presentation on theme: "{ Semester Exam Review AP Calculus. Exam Topics Trig function derivatives."— Presentation transcript:

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

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