AP Calculus AB Practice Questions

Overview

• This document is a set of flashcards designed to help students practice AP Calculus AB concepts via Quizlet.
• The flashcards cover various calculus rules, derivative concepts, and integral applications.

Key Calculus Concepts

Derivatives

• Product Rule: Used when taking the derivative of a product of two functions.
• Implicit Differentiation: Used when both x and y are present on one side of an equation.
• L'Hopital's Rule: Applied when evaluating limits that result in indeterminate forms.

Rules and Definitions

• Increasing Function: First derivative is positive.
• Decreasing Function: First derivative is negative.
• Concave Up: Second derivative is positive.
• Concave Down: Second derivative is negative.
• Critical Points: Occur when the first derivative is zero.
• Points of Inflection: Occur when the second derivative is zero.

Calculus Applications

• Continuity Requirements:
  1. Limit must exist.
  2. Function must be defined.
  3. Function and limit must agree.
• Finding f’(x): Take derivative and substitute the given value.
• Area Between Curves: Subtract bottom curve from top curve, integrate.
• Equation of Tangent Line:
  • Requires point (x, y).
  • Use slope from the derivative at the point.

Integral Calculus

• Integration for Velocity and Distance:
  • To find distance from velocity, integrate.
  • For velocity from distance, differentiate.
• Riemann Sums:
  • Left-handed: Skip last number, arrows to left and down.
  • Right-handed: Skip first number, arrows to right and down.
  • Trapezoid and Midpoint methods are also discussed.

Asymptotes and Discontinuities

• Vertical Asymptotes: Occur when the denominator is zero.
• Removable Discontinuities: Factors that cancel out.
• Horizontal Asymptotes: Evaluated as limits at infinity.

Theorems

• Intermediate Value Theorem: Continuous functions hit every y-value between endpoints.
• Mean Value Theorem: Used to find a point where the tangent slope equals the secant slope.

Miscellaneous

• Second Fundamental Theorem of Calculus: Remember derivative of the bounds.
• Speed Considerations:
  • Speed increasing: First and second derivatives have the same sign.
  • Speed decreasing: First and second derivatives have different signs.

Additional Resources

• Links to related study sets and guides for further learning are provided.

Created By

• Teacher: mamackay

These notes capture the essential formulas and rules needed for AP Calculus AB, as represented in the Quizlet flashcard set. Use them as a reference to understand and apply calculus concepts in practice questions.