AP Calculus AB Study Guide Units 1-8
What is the definition of a derivative?
What does the intermediate value theorem state?
If the function f(x) is continuous on [a,b], and y is a number between f(a) and f(b), then there exists at least one number x=c in the open interval (a,b) such that f(c)=y.
What does the mean value theorem state?
If the function f(x) is continuous on [a,b], and the first
derivative exists on the interval (a,b) and f(a)=f(b), then there is at least one number x=c in (a,b) such that f'(c)=0.
What does Rolle's Theorem state?
If the function f(x) is continuous on [a,b], and the first
derivative exists on the interval (a,b) and f(a)=f(b), then there is at least one number x=c in (a,b) such that f'(c)=0.
What does the Extreme Value Theorem state?
If the function f(x) is continuous on [a,b], then the function is guaranteed to have an absolute maximum and an absolute minimum on the interval.
derivative of x^n derivative of sinx
cosx
derivative of cosx
-sinx
derivative of tanx
sec^2x
derivative of cotx
-csc^2x
derivative of secx
secxtanx
derivative of cscx
-cscxcotx
derivative of lnu
derivative of e^u
e^u du/dx
Chain Rule
Product Rule
What is the definition of a derivative?
What does the intermediate value theorem state?
If the function f(x) is continuous on [a,b], and y is a number between f(a) and f(b), then there exists at least one number x=c in the open interval (a,b) such that f(c)=y.
What does the mean value theorem state?
If the function f(x) is continuous on [a,b], and the first
derivative exists on the interval (a,b) and f(a)=f(b), then there is at least one number x=c in (a,b) such that f'(c)=0.
What does Rolle's Theorem state?
If the function f(x) is continuous on [a,b], and the first
derivative exists on the interval (a,b) and f(a)=f(b), then there is at least one number x=c in (a,b) such that f'(c)=0.
What does the Extreme Value Theorem state?
If the function f(x) is continuous on [a,b], then the function is guaranteed to have an absolute maximum and an absolute minimum on the interval.
derivative of x^n derivative of sinx
cosx
derivative of cosx
-sinx
derivative of tanx
sec^2x
derivative of cotx
-csc^2x
derivative of secx
secxtanx
derivative of cscx
-cscxcotx
derivative of lnu
derivative of e^u
e^u du/dx
Chain Rule
Product Rule
