AP Calculus AB Key Concepts

Front

Intermediate Value Theorem (IVT) conditions

Back

1. f is continuous on the closed interval [a, b] 2. f(a) ≠ f(b) 3. k is between f(a) and f(b)

Front

Squeeze Theorem

Back

If f(x) ≤ g(x) ≤ h(x) and as x → a, f(x) → L and h(x) → L, then g(x) → L.

Front

lim (x → -∞) e^x

Back

0

Front

Definition of the derivative

Back

f'(x) = lim (h → 0) [(f(x+h) - f(x))/h] (limit of the difference quotient)

Front

Alternate form of the derivative

Back

f'(x) = lim (x → b) [(f(x) - f(b))/(x - b)]

Front

Average rate of change

Back

The slope of the secant line between two points: (f(b) - f(a))/(b - a)

Front

Non-differentiability conditions

Back

1. f not continuous at x = a 2. The graph of f has a “corner” or “cusp” at x = a 3. The graph of f has a vertical tangent at x = a

Front

position

Back

s(t)

Front

Particle at rest condition

Back

v(t) = 0

Front

d/dx(c)

Back

0