Derivative test

clarifications for each "f" feature

critical points on f

f^I(x)=0 or und

f is inc

f^I(x)>0

f is dec

f^I(x)<0

f has rel max

f^I changes sign from pos to neg

f has rel min

f^I changes sign from neg to pos

potential inflection points

f^II(x)=0 or und

true inflection points…

f^II number line changes sign from pos to neg or neg to pos

f^I changes from inc to dec or dec to inc

f is concave up

f^II(x)>0

the slope on f^I is pos (think swirlies)

f is concave down

f^II(x)<0

the slope on f^I is neg

absoulte max

create table and find which f(x) is greatest using the end points and the critical points of f

absoulte min

create table and find which f(x) is lowest using the end points and the critical points of f

total distance traveled

add up the differences between f(x) from the table using end points and critical points