AP Calculus AB

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Derivatives (1st Semester)

1. Concept of the Derivative

• Graphically, numerically and algebraically
• Instantaneous rate of change
• Limit of the difference quotient: the definition
• Relationship between differentiability and continuity

2. Derivative at a point

• Slope of a curve at a point
• Tangent line and linear approximation
• Instantaneous rate of change
• Approximate rate of change calculated from tables and charts

3. Derivative as a function

• Comparison of graphs of a function and its derivative
• The Mean Value Theorem and its consequences
• Equations involving derivatives; verbal descriptions of functions and their derivatives

4. Second derivatives

• Comparisons of the graphs of a function with its first and second derivative
• Concavity
• Inflection points

5. Applications of derivatives

• Analysis of curves
• Optimization, global and local
• Modeling rates of change, including related rates
• Implicit differentiation, including its use for inverse functions
• The derivative as a rate of change in applied contexts, including motion, velocity speed and acceleration

6. Computation of the derivative

• Derivatives of power, trigonometric, logarithmic, exponential, and inverse trigonometric functions
• Sum, product, quotient and chain rules

Announcements
• Remind 101

Text: @skincalc to the number 81010

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