AP Notes, Outlines, Study Guides, Vocabulary, Practice Exams and more!

AP Calculus Theorems Flashcards

This set goes over all those pesky theorems, rules, and properties that are useful to know when it comes to the AP test.

Terms : Hide Images
9860907636Definition of Continuity1. lim x→c f(x) exists. 2. f(c) exists. 3. lim x→c f(x) = f(c)0
9860907637When 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→c1
9860907638Intermediate Value TheoremIf 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) = k2
9860907639Definition of a Derivativelim h→0 (f(x+h) - f(x)) / h3
9860907640Product Ruled/dx (f(x) g(x)) = f(x)g'(x) + g(x) f'(x)4
9860907641Quotient Ruled/dx (g(x)/ h(x)) = (h(x) g'(x) - g(x) h'(x))/ h(x)^25
9860907642Chain Ruled/dx f(g(x)) = f'(g(x)) g'(x)6
9860907643Extrema Value TheoremIf f is continuous on the closed interval [a, b], then f has both a maximum and a minimum on the interval.7
9860907644The first derivative gives what?1. critical points 2. relative extrema 3. increasing and decreasing intervals8
9860907645The second derivative gives what?1. points of inflection 2. concavity9
9860907646Rolle's TheoremLet 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)= 010
9860907647Mean Value Theoremf'(c) = (f(b) - f(a))/ (b - a)11
9860907648Fundamental Theorem of CalculusThe integral on (a, b) of f(x) dx = F(b) - F(a)12
9860907649Mean Value Theorem (Integrals)The integral on (a, b) of f(x) dx = f(c) (b - a)13
9860907650Average Value Theorem1/ (b-a) times the integral on (a, b) of f(x) dx14
9860907651Second Fundamental Theorem of CalculusIf 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)15
9860907652Derivative of an Inverse Functiong'(x) = 1/ f'(g(x)) where g(x) is the inverse of f(x)16

Need Help?

We hope your visit has been a productive one. If you're having any problems, or would like to give some feedback, we'd love to hear from you.

For general help, questions, and suggestions, try our dedicated support forums.

If you need to contact the Course-Notes.Org web experience team, please use our contact form.

Need Notes?

While we strive to provide the most comprehensive notes for as many high school textbooks as possible, there are certainly going to be some that we miss. Drop us a note and let us know which textbooks you need. Be sure to include which edition of the textbook you are using! If we see enough demand, we'll do whatever we can to get those notes up on the site for you!