Calc Theorems
Studied by 8 people
Call Kai
Learn
Practice Test
Spaced Repetition
Match
Flashcards
Knowt Play1/6
Earn XP
Name | Mastery | Learn | Test | Matching | Spaced | Call with Kai |
|---|
No analytics yet
Send a link to your students to track their progress
7 Terms
Extreme Value Theorem
If f is continuous on a closed interval [a,b], then f has both an absolute minimum and absolute maximum
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 value c in the closed interval [a,b] such that f(c) = k
Mean Value Theorem
If f is continuous on the closed interval [a,b] and differentiable on the open interval (a,b), then there exists a value c in (a,b) such that…
![<p>If f is continuous on the closed interval [a,b] and differentiable on the open interval (a,b), then there exists a value c in (a,b) such that…</p>](https://knowt-user-attachments.s3.amazonaws.com/7df69652-e464-4c8d-9af5-2d0977ce55f7.jpg)
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 value c in (a,b) such that f ' (c) = 0
![<ul><li><p>Let f be continuous on the closed interval [a,b] and differentiable on the open interval (a,b)</p></li><li><p>If f(a) = f(b), then there is at least one value c in (a,b) such that f ' (c) = 0</p></li></ul>](https://knowt-user-attachments.s3.amazonaws.com/bca43a7e-609d-4bf6-9e4f-10d31348ef4a.jpg)
The Fundamental Theorem of Calculus
If f(x) is continuous and integrable on [a,b] and F(x) is the antiderivative of f(x) then…
![<p>If f(x) is continuous and integrable on [a,b] and F(x) is the antiderivative of f(x) then…</p>](https://knowt-user-attachments.s3.amazonaws.com/09d09e6f-6295-48f8-b065-3bf546a3d64d.png)
FTC Part 2
If f is continuous on the open interval I containing a, then for every x in I
Extension of FTC Part 2
Note 
Flashcards (61)