Term
Conditions for continuity at a point 

Definition
Function exists
Limit exists
Limit is equal to function 


Term
Conditions where a function is not differentiable 

Definition
Corners / Cusps
Vertical tangents
Discontinuities 


Term
Definition of a corner or cusp 

Definition
Slope from left does not equal slope from right 


Term

Definition
(First)*(derivative of second)+(second)*(derivative of first)
or
uv'+vu' 


Term

Definition
(bottom)(derivative of top)  (top)(derivative of bottom) all over (bottom)^{2} 


Term
Intermediate value theorem  functions 

Definition
if f(x) is continuous on (a,b)
Then f(x) will pass through every value between f(a) and f(b) at least once on the interval (a,b) 


Term
Intermediate value theorem  derivatives 

Definition
if f(x) is differentiable on (a,b)
then f'(x) takes every value between f'(a) and f(b) at least once on the interval (a,b) 


Term
If it's differentiable... 

Definition

