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

Mathematics
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Familiar with the derivative ? can you take the derivative of f(x), if so, what do you get ?
2
what are the roots of 2 ? where does it cross the x axis

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Other answers:

at y=0???
can y ever be zero if it always equals 2 ?
nope
any max extrema then ?
abs*
im kinda of confused by ur question :[
u got x=2 put it in f(x) to find the extrema
1 ?
thats correct :)
thats it?
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.....
but you c in my book it has an answer or answers of min (0,-3) and max (2,1)
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)
*local = absolute
whenever we don't get global extrema, we put endpoints....remember this.
i am utterly confused :[
lets start over ?
yes please :]
ok, absolute extrema means max or min points in the given interval.
now to find min or max values, you take derivative of function and set it =0
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 ?
ok
or if its like 1/0 right?
in that case, we can find 'local' or 'absolute' values at the endpoints, they become min/max values.
yes.
so 2=0
i can't think of an example when u get 1/0 after taking the derivative.
here , you get f'(x) =2 we cannot equate this to 0
because 2 can never =0 hence there is no extrema, or as we say, no global extrema
but we can find absolute extrema, that is min/max in GIVEN INTERVAL
how do we find these?
one of the end-point is x=2 there what is f(x) = ?
1?
so the point is (2,1) and this is one of the extrema we don't know yet whether this is max or min
now put other end point, x=0 what is f(x)
wait where did we get x=0?
[0,2]
your interval [0,2]
thats where i got x=2 also earlier
ooooooooo okay there will be 3 extrema right???
how come 3 ? one for x=2, and one for x=0
o yeah my bad -_- :]
we do the same for 0 right ???? plug it into the orig equation? right?
you could just say there's no global min/max since the function is linear right?..
yes.
to both
k, thanks. double checking.
now put other end point, x=0 what is f(x)
-3?
so the other point is ?
and which one should be min and which one should be max ?
0,-3 is min the other is max?
yes, thats correct. clear with every step ?
yes sir or mam! :]
thanks so much!
your welcome ^_^
:]

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