anonymous
  • anonymous
locate the absolute extrema of the function (if any exist) over the interval. f(x)=2x-3 [0, 2]
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
Familiar with the derivative ? can you take the derivative of f(x), if so, what do you get ?
anonymous
  • anonymous
2
anonymous
  • anonymous
what are the roots of 2 ? where does it cross the x axis

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

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