AP Calculus AB/BC Formula and Concept Cheat Sheet

A set of vocabulary flashcards to help review key concepts in AP Calculus AB/BC.

Limit of a Continuous Function

If f(x) is continuous for all real numbers, then lim x→c f(x) = f(c).

Limit of a Rational Function

If f(x) = p(x)/q(x) and q(c)=0, then lim x→c f(x) does not exist or is ±∞.

Vertical Asymptote

Occurs at x = c if lim x→c f(x) = ±∞.

Continuous at c

A function f(x) is continuous at c if lim x→c f(x) exists, f(c) exists, and lim x→c f(x) = f(c).

Removable Discontinuity

Occurs if lim x→c f(x) = L and f(c) is undefined.

Non-Removable Discontinuity

Can occur as jumps or asymptotes, where limits do not match or diverge.

Intermediate Value Theorem

If f is continuous on [a, b] and k is between f(a) and f(b), then there is a c in [a, b] such that f(c) = k.

Average Rate of Change

The average rate of change of a function f on [a, b] is given by m = (f(b) - f(a)) / (b - a).

Derivative Definition

f'(x) = lim h→0 [f(x+h) - f(x)] / h.

Differentiability and Continuity

If f(x) is differentiable at x=c, then it is continuous at x=c.

Tangent Line Equation

The equation of the tangent line at (a, f(a)) is y - f(a) = f'(a)(x - a).

Mean Value Theorem

If f is continuous on [a, b] and differentiable on (a, b), then there exists a c such that f'(c) = (f(b) - f(a)) / (b - a).

Rolle's Theorem

If f is continuous on [a, b], differentiable on (a, b), and f(a) = f(b), then there exists at least one c in (a, b) such that f'(c) = 0.

Velocity Function

v(t) = x'(t).

Acceleration Function

a(t) = v'(t) = x''(t).

Critical Value

f'(c) = 0 or f' is undefined.

Second Derivative Test

If f''(c) > 0, then f(c) is a relative minimum; if f''(c) < 0, then f(c) is a relative maximum.