Monotonic conditions. Extremum of functionTheorem 1. Let function if and only if Definition 1. A function or simply increasing (resp. decreasing) on an interval then Definition 2. A function interval then Theorem 2. Let (a) if (b)if Definition 3. A neighborhood of a point Definition 4. A function
|
be continuous on [a, b] and differentiable on (a, b). 
for all 
.
if and only if 
, if 
(resp. 
).
(resp. 
).
is an open interval containing 
is a neighborhood of 
.
is said to attain a relative maximum (minimum) at a point 
(
) in a certain neighborhood of 
such that 
.
