increasing and decreasing functions

decreasing function

A function is decreasing on an interval if f(x2)<f(x1) whenever x2>x1

decreasing if

a function is decreasing if mtan=IROC is negative

increasing if

a function is increasing if mtan=IROC is positive

increasing function

a function is increasing on an interval if f(x2)>f(x1) whenever x2>x1

sequence

a function whose domain is the set of natural numbers, or a subset thereof

IROC

f(x+h)-f(x)/h

AROC

f(x2)-f(x1)/x2-x1

decreasing function x and y

if you plug in bigger x and get smaller y

increasing function x and y

if you plug in bigger x than there is bigger y

local extrema

may occur when the slope of the tangent line mtan=IROC=0 or mtan= does not exist

local min

when f(x) changes from decline to incline

local max

when f(x) changes from incline to decline