keywords:
Bookmark and Share



Front Back
Definition of Continuity
1. lim x→c f(x) exists.
2. f(c) exists.
3. lim x→c f(x) = f(c)
When does the limit not exist?
1. f(x) approaches a different number from the right as it does from the left as x→c 
2. f(x) increases or decreases without bound as x→c
3. f(x) oscillates between two fixed values as x→c
Intermediate Value Theorem
If f is continuous on the closed interval [a,b] and k is any number between f(a) and f(b) then there is at least one number c in [a, b] such that f(c) = k
Chain Rule
d/dx f(g(x)) = f'(g(x)) g'(x)
Extrema Value Teorem
f f is continuous on the closed interval [a, b], then f has both a maximum and a minimum on the interval.
The First Derivative gives what?
1. critical points
2. relative extrema
3. increasing and decreasing intervals
The Second Derivative gives what?
1. points of inflection
2. concavity
Rolle's Theorem
Let f be continuous on the closed interval [a, b] and differentiable on the open interval (a, b). If f(a) = f(b) then there is at least one number c in (a, b) such that f'(c)= 0
Second Fundamental Theorem of Calculus
If f is continuous on an open interval containing a, then for every x in the interval the derivative of the the integral of f(x) dx on said interval is equal to f(x)
The Fundamental Theorem of Caluculus
Definition of a Derivative
Product Rule
Quotient Rule
Average Value Theorem
Mean Value Theorem (Integrals)
Mean Value Theorem
Derivative of an Inverse
x of y cards