Question

locate the absolute extrema of the function (if any exist) over the interval. f(x)=2x-3 [0, 2]

Answer 1

Familiar with the derivative ? can you take the derivative of f(x), if so, what do you get ?

Answer 2

2

Answer 3

what are the roots of 2 ? where does it cross the x axis

Answer 4

at y=0???

Answer 5

can y ever be zero if it always equals 2 ?

Answer 6

nope

Answer 7

any max extrema then ?

Answer 8

abs*

Answer 9

im kinda of confused by ur question :[

Answer 10

u got x=2
put it in f(x) to find the extrema

Answer 11

1 ?

Answer 12

thats correct :)

Answer 13

thats it?

Answer 14

wait.
for extrema, u take derivative and equate it to 0
means you do, f'(x)=0
but you got f'(x) = 2
hence there is no extrema.....

Answer 15

but you c in my book it has an answer or answers of min (0,-3) and max (2,1)

Answer 16

i know, there is no global extrema,
and so, here we find local extrema by substituting the endpoints.
so put x=0 and x=2
and find f(x)

Answer 17

*local = absolute

Answer 18

whenever we don't get global extrema, we put endpoints....remember this.

Answer 19

i am utterly confused :[

Answer 20

lets start over ?

Answer 21

yes please :]

Answer 22

ok, absolute extrema means max or min points in the given interval.

Answer 23

now to find min or max values, you take derivative of function and set it =0

Answer 24

then you get values of x for which the function is min/max.
if f'(x) cannot be equal to 0, then there is no global extrema
ok ?

Answer 25

ok

Answer 26

or if its like 1/0 right?

Answer 27

in that case, we can find 'local' or 'absolute' values at the endpoints, they become min/max values.

Answer 28

yes.

Answer 29

so 2=0

Answer 30

i can't think of an example when u get 1/0 after taking the derivative.

Answer 31

here , you get f'(x) =2
we cannot equate this to 0

Answer 32

because 2 can never =0
hence there is no extrema, or as we say, no global extrema

Answer 33

but we can find absolute extrema, that is min/max in GIVEN INTERVAL

Answer 34

how do we find these?

Answer 35

one of the end-point is x=2
there what is f(x) = ?

Answer 36

1?

Answer 37

so the point is (2,1) and this is one of the extrema
we don't know yet whether this is max or min

Answer 38

now put other end point, x=0
what is f(x)

Answer 39

wait where did we get x=0?

Answer 40

[0,2]

Answer 41

your interval [0,2]

Answer 42

thats where i got x=2 also earlier

Answer 43

ooooooooo okay there will be 3 extrema right???

Answer 44

how come 3 ?
one for x=2, and one for x=0

Answer 45

o yeah my bad -_- :]

Answer 46

we do the same for 0 right ???? plug it into the orig equation? right?

Answer 47

you could just say there's no global min/max since the function is linear right?..

Answer 48

yes.

Answer 49

to both

Answer 50

k, thanks. double checking.

Answer 51

now put other end point, x=0
what is f(x)

Answer 52

-3?

Answer 53

so the other point is ?

Answer 54

and which one should be min and which one should be max ?

Answer 55

0,-3 is min the other is max?

Answer 56

yes, thats correct.
clear with every step ?

Answer 57

yes sir or mam! :]

Answer 58

thanks so much!

Answer 59

your welcome ^_^

Answer 60

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