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{ Semester Exam Review AP Calculus

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Exam Topics

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Trig function derivatives

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Differentiate: Co-Functions: Negative!!

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

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Derivatives by limits:

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Rate of Change: Average vs. Instantaneous

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

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Writing Equation of Tangent Line

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Displacement/Velocity/Acceleration

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Implicit Differentiation:

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Differentiate implicitly:

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

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

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Useful Related Rates Formulas

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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

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To Prove Continuity:

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Trapezoidal Rule/Riemann Sums

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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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2.1 Derivatives and Rates of Change. The slope of a line is given by: The slope of the tangent to f(x)=x 2 at (1,1) can be approximated by the slope of.

2.1 Derivatives and Rates of Change. The slope of a line is given by: The slope of the tangent to f(x)=x 2 at (1,1) can be approximated by the slope of.

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