AP Calc Theorems & Rules

Limit exists

Limit exists when both the one-sided limits are equal to the same number

The Squeeze Theorem

if f(x) ≤ g(x) ≤ h(x) and if f(x) and h(x) have the same limit, then g(x) has the same limit

Average Rate of Change

f(b) - f(a)/ b-a

Definition of Derivative (limit)

f’(x) = lim (h → 0) (f(x + h) - f(x))/h

Mean Value Theorem

if f(x) is continuous on \[a,b\], then there exists a value x = c such that (image)

* Rolle’s Theorem is MVT when f(a) = f(b) making f’(c) is 0

Average Value

Fundamental Theorem of Calculus

2nd Fundamental Theorem of Calculus

Intermediate Value Theorem (IVT)

if f(x) is continuous on \[a,b\] and m is a number between a and b, then at x=c, there exists f(c) = m

Extreme Value Theorem

If a function *f(x)* is continuous on a closed interval \[ *a, b*\], then *f(x)* has at least one maximum and minimum on \[ *a, b*\]