lilly21
locate the absolute extrema of the function (if any exist) over the interval. f(x)=2x3 [0, 2]



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

lilly21
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2

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

lilly21
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at y=0???

infoshark
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can y ever be zero if it always equals 2 ?

lilly21
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nope

infoshark
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any max extrema then ?

infoshark
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abs*

lilly21
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im kinda of confused by ur question :[

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

lilly21
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1 ?

hartnn
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thats correct :)

lilly21
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thats it?

hartnn
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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.....

lilly21
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but you c in my book it has an answer or answers of min (0,3) and max (2,1)

hartnn
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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
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*local = absolute

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

lilly21
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i am utterly confused :[

hartnn
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lets start over ?

lilly21
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yes please :]

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

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

hartnn
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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 ?

lilly21
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ok

lilly21
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or if its like 1/0 right?

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

hartnn
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yes.

lilly21
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so 2=0

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

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

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

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

lilly21
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how do we find these?

hartnn
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one of the endpoint is x=2
there what is f(x) = ?

lilly21
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1?

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

lilly21
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wait where did we get x=0?

hartnn
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[0,2]

jaersyn
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your interval [0,2]

hartnn
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thats where i got x=2 also earlier

lilly21
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ooooooooo okay there will be 3 extrema right???

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

lilly21
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o yeah my bad _ :]

lilly21
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we do the same for 0 right ???? plug it into the orig equation? right?

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

hartnn
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yes.

hartnn
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to both

jaersyn
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k, thanks. double checking.

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

lilly21
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3?

hartnn
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so the other point is ?

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

lilly21
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0,3 is min the other is max?

hartnn
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yes, thats correct.
clear with every step ?

lilly21
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yes sir or mam! :]

lilly21
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thanks so much!

hartnn
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your welcome ^_^

lilly21
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:]