Question

Can someone tell me why x=4 isn't a local maximum but (-1,37) is an abs maximum (its consider some type of maximum)?

Answer 1

Here is a picture

Answer 2

local extrema do not exist at the endpoints

Answer 3

if P is some point on the curve, then you need to have other points on both sides of point P to have P be considered to be a local extrema

Answer 4

but (-1,37) is an endpoint

Answer 5

since y = 37 is the largest output, this means it is an abs max

it's possible for absolute extrema to exist at the endpoints

Answer 6

okay thanks

Answer 7

see attached

Answer 8

sorry I left out a local min

Answer 9

Thanks for drawing it out for me. I appreciate it

Answer 10

you're welcome