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

- anonymous

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

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- anonymous

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

- anonymous

2

- anonymous

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

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## More answers

- anonymous

at y=0???

- anonymous

can y ever be zero if it always equals 2 ?

- anonymous

nope

- anonymous

any max extrema then ?

- anonymous

abs*

- anonymous

im kinda of confused by ur question :[

- hartnn

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

- anonymous

1 ?

- hartnn

thats correct :)

- anonymous

thats it?

- hartnn

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.....

- anonymous

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

- hartnn

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)

- hartnn

*local = absolute

- hartnn

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

- anonymous

i am utterly confused :[

- hartnn

lets start over ?

- anonymous

yes please :]

- hartnn

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

- hartnn

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

- hartnn

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 ?

- anonymous

ok

- anonymous

or if its like 1/0 right?

- hartnn

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

- hartnn

yes.

- anonymous

so 2=0

- hartnn

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

- hartnn

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

- hartnn

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

- hartnn

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

- anonymous

how do we find these?

- hartnn

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

- anonymous

1?

- hartnn

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

- hartnn

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

- anonymous

wait where did we get x=0?

- hartnn

[0,2]

- anonymous

your interval [0,2]

- hartnn

thats where i got x=2 also earlier

- anonymous

ooooooooo okay there will be 3 extrema right???

- hartnn

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

- anonymous

o yeah my bad -_- :]

- anonymous

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

- anonymous

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

- hartnn

yes.

- hartnn

to both

- anonymous

k, thanks. double checking.

- hartnn

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

- anonymous

-3?

- hartnn

so the other point is ?

- hartnn

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

- anonymous

0,-3 is min the other is max?

- hartnn

yes, thats correct.
clear with every step ?

- anonymous

yes sir or mam! :]

- anonymous

thanks so much!

- hartnn

your welcome ^_^

- anonymous

:]

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