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