Question

difference between the relative extrema on an open interval vs closed interval? define the relationship between f'(x) and functions local max or min. calculus ppl only

Answer 1

@Ultrilliam

Answer 2

@zarkam21

Answer 3

why is this in comp sci

Answer 4

also @Angle Calculus Question

Answer 5

bc i cant find an old math question

Answer 6

i posted

Answer 7

Gabe, to find it go to the subject, you will see the question pop up right in the question box

Answer 8

^example

Answer 9

i got u

Answer 10

i found it but its a tuff question i want to keep it up lmao

Answer 11

then I'll just move this to mathematics lol

Answer 12

wait will that destroy my old one

Answer 13

do u know how to explain this. my teacher wants a lengthy explaination. so at least 3-4 sentences

Answer 14

Nah, I already did it, they'll both be open

Answer 15

and I let Angle know about the question to help when she can

Answer 16

ok thanks

Answer 17

https://www.math.hmc.edu/calculus/tutorials/extrema/

Answer 18

http://www.swl.k12.oh.us/Downloads/3-1%20Extrema%20on%20an%20Interval.pdf

Answer 19

So.

A relative minimum is a point where the points just around it are all higher than this point. A relative maximum is a point where the points just around it are all lower than this point.

So on an open interval, the end points are not included in the considered points. So the end points are not relative extrema.
On the other hand, on the closed interval, we can take them into consideration. For an end point, there are three options, either it's going to increase, decrease, or stay the same.
If it increases, then it is a relative minimum because the points around it are all higher. If it decreases, then it is a relative maximum because the points around it are all lower. And if it stays the same, then it is not a relative extrema.

This should help to answer your first question.

Answer 20

A relative minimum is a point where the points just around it are all higher than this point. A relative maximum is a point where the points just around it are all lower than this point.

If you are at a relative minimum (on an open interval for an easier example), then the points coming from the left are all higher than it and coming to meet that point, so the slope is negative. Following this, the points going out to the right of the relative minimum are also all higher than this minimum, so the slope is positive.
If a slope goes from negative to positive, then it needs to have crossed zero at some time. (see intermediate value theorem).

Something similar happens with the relative maximum.
Therefore, all relative extrema have a f'(x) value of 0