Stuff you MUST know for the AP Calculus Exam on the morning of Tuesday, May 9, 2007 By Sean Bird

Curve sketching and analysis y = f(x) must be continuous at each: critical point: = 0 or undefined. And don’t forget endpoints local minimum: goes (–,0,+) or (–,und,+) or > 0 local maximum: goes (+,0,–) or (+,und,–) or < 0 point of inflection: concavity changes goes from (+,0,–), (–,0,+), (+,und,–), or (–,und,+)

Basic Derivatives

Basic Integrals

More Derivatives

Differentiation Rules Chain Rule Product Rule Quotient Rule

The Fundamental Theorem of Calculus Corollary to FTC

Intermediate Value Theorem. Mean Value Theorem. If the function f(x) is continuous on [a, b], AND the first derivative exists on the interval (a, b), then there is at least one number x = c in (a, b) such that If the function f(x) is continuous on [a, b], and y is a number between f(a) and f(b), then there exists at least one number x = c in the open interval (a, b) such that f(c) = y.

If the function f(x) is continuous on [a, b], AND the first derivative exists on the interval (a, b), then there is at least one number x = c in (a, b) such that If the function f(x) is continuous on [a, b], AND the first derivative exists on the interval (a, b), AND f(a) = f(b), then there is at least one number x = c in (a, b) such that f '(c) = 0. Mean Value Theorem & Rolle’s Theorem

Approximation Methods for Integration Trapezoidal Rule Simpson’s Rule Simpson only works for Even sub intervals (odd data points) 1/3 ( )

Theorem of the Mean Value i.e. AVERAGE VALUE If the function f(x) is continuous on [a, b] and the first derivative exists on the interval (a, b), then there exists a number x = c on (a, b) such that This value f(c) is the “average value” of the function on the interval [a, b].

Solids of Revolution and friends Disk Method Washer Method General volume equation (not rotated) Arc Length * bc topic

Distance, Velocity, and Acceleration velocity =(position) (velocity) speed = displacement = average velocity = acceleration = *velocity vector = *bc topic

Values of Trigonometric Functions for Common Angles 0–10π,180° ∞ 01,90°,60° 4/33/54/553° 1,45° 3/44/53/537°,30° 0100° tan θcos θsin θθ π/3 = 60° π/6 = 30° sine cosine

Trig Identities Double Argument

Double Argument Pythagorean sine cosine