I have a question where I have to figure out endpoints. The function is x^2-4x+1 x is a set of [0,3]
now the book says the endpoint at f(0) is 1 and is the endpoint max. f(3) is -2 and is also the endpoint max. I know how to get the critical points but I am a little confused as when dealing with endpoints is it always just a max you are dealing with? Is there such a thing as an endpoint min? Is there somewhere that explains the difference between these and absolute min, local min and the difference between absolute max, local max? I think a clarification on these terms would help and wonder if there is a reference online somewhere that explains in english
If the endpoints are just the points at the extremities of your interval (i.e 0 and 3) then f(0) and f(3) are the endpoints for the mapping.
The end points in the above context are unique so this means its kind of pointless having a min and max endpoint.