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

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

{ Semester Exam Review AP Calculus

Exam Topics

Trig function derivatives

Differentiate: Co-Functions: Negative!!

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

Derivatives by limits:

Rate of Change: Average vs. Instantaneous

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

Writing Equation of Tangent Line

Displacement/Velocity/Acceleration

Implicit Differentiation:

Differentiate implicitly:

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

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

Useful Related Rates Formulas

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

To Prove Continuity:

Trapezoidal Rule/Riemann Sums

 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

Download ppt "{ Semester Exam Review AP Calculus. Exam Topics Trig function derivatives."

Similar presentations