Question

I have a question regarding max and min. How do i know wheter a function has a abso max/min or rel mx/min?

Answer 1

okay, can you take a look at this graph i drew

Answer 2

My book asks me to find the critical number and determine whether the function has a reelative max., relative min., absolute max., absolute min, on these crtical numbers

Answer 3

The books answers are as follows:

1, absolute max (and rel. max)
2, absolute min (and rel. min)
3, absolute max (and rel. max)

Answer 4

Well, let me re-phrase....The absolute min max will be the endpoints of the function,
The relative min/max will be those peaks and valleys that occur between the endpoints

Answer 5

Why, does the book have the answer as being absolute max and min. This isnt a closed interval graph is it?

Answer 6

and how come the book has abso max/ min and also have rel. max/min in parentheses?

Answer 7

?

Answer 8

I can't confirm, but it seems like now it has one absolute min, two absolute max, and two relative min

Answer 9

Okay, i an see, that but, if you could help me understand why the these critcal point would be considered absolute max and min and not just rel. max and min, considering that this is not a graph over a closed interval

Answer 10

can you help me with my question?

Answer 11

What are the critical numbers?

Answer 12

i know critical numbers are where the derivative is equal to zero

Answer 13

OK, turning points. So what did your derivative tell you?

Answer 14

well , i dont have a function, i only have a graph, which i posted

Answer 15

Im really just confused over when to lable somehting as an abso max or min or rel. max or min

Answer 16

OK, so what is going on at 0 and 4, I can't tell from the graph?

Answer 17

Well, those are open circles right, which means this is an open interval?

Answer 18

Meaning the graph doesn't include those points, correct?

Answer 19

correct

Answer 20

See i thought that if i was asked to find the max and min or a graph with an open interval, there could only be relative extrema.

Answer 21

Who told u that?

Answer 22

well, nonbody told me that, from my reading i always saw that when a book talked about absolute max, and min, it talked about it with regards to a closed interval. I mean, the book also talked about realtive max and min over closed intervals, but how is it that i determin whether the answer to a question such as the one i got is relative or absolute?

Answer 23

As far as I can see on the bit of graph you posted there are 3 turning points, two tops and a bottom.

Answer 24

The highest top is the absolute max and the lower one the relative (or local) max.

And there is only one bottom so it is the absolute bottom.

Answer 25

my graph may be off, but both tops are eqaul

Answer 26

How come you say that the tops and bottoms are absolute max and min, and not relative max and min, or are they both

Answer 27

Max just means highest value of y and min just means lowest. Relative is in between.

Answer 28

oh so relative could be considerde a smaller hill or smaller valley compared to the absolute hill or vallyey

Answer 29

With a lower value of y for a top and a higher value of y for a bottom.

Answer 30

got it thanks

Answer 31

Normally to test this, when you have a suitable function, you take a second derivative and then the sketch is just for reference or quick check.

Answer 32

Like here: http://en.wikipedia.org/wiki/Second_derivative_test

But don't worry if you haven't done this yet.

Answer 33

Pic.

Answer 34

That was actually a really helpful graph, thanks