Stuff you MUST know cold for AP Calculus!

Note: Letters like a, b, c, d, m, and n are traditionally used to represent constants.

Letters like f, g, h, u, v, x, and y and traditionally used to represent variables or functions.


Basic Derivatives

 

More Derivatives

 

If a function is differentiable,

then it is continuous.


Definitions of Derivative

 

Differentiation Rules

Chain Rule

If , then .

OR

 

Product Rule

 

Quotient Rule

 

“PLUS A CONSTANT!”

 

The Fundamental Theorem of Calculus

where

 

Corollary to the FTC

 

Intermediate Value Theorem

If function f is continuous for all x in the closed interval , and y is a number between  and , then there is a number  in  for which .

 


Rolle’s Theorem

If  f is differentiable for all values of x in the open interval , and  f is continuous at  and at , and  ,

then there is at least one number  in  such that .

 

Mean Value Theorem

If f is differentiable for all values of x in the open interval , and f is continuous at  and , then there is at least one number  in  such that

 

Trapezoidal Rule

 

Distance, Velocity, and Acceleration

If distance, velocity and acceleration are represented by s, v, and a, respectively, then  and .

 

l'Hôpital’s Rule

If

then