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

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infosharkBest ResponseYou've already chosen the best response.0
Familiar with the derivative ? can you take the derivative of f(x), if so, what do you get ?
 one year ago

infosharkBest ResponseYou've already chosen the best response.0
what are the roots of 2 ? where does it cross the x axis
 one year ago

infosharkBest ResponseYou've already chosen the best response.0
can y ever be zero if it always equals 2 ?
 one year ago

infosharkBest ResponseYou've already chosen the best response.0
any max extrema then ?
 one year ago

lilly21Best ResponseYou've already chosen the best response.1
im kinda of confused by ur question :[
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
u got x=2 put it in f(x) to find the extrema
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
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.....
 one year ago

lilly21Best ResponseYou've already chosen the best response.1
but you c in my book it has an answer or answers of min (0,3) and max (2,1)
 one year ago

hartnnBest ResponseYou've already chosen the best response.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)
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
whenever we don't get global extrema, we put endpoints....remember this.
 one year ago

lilly21Best ResponseYou've already chosen the best response.1
i am utterly confused :[
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
ok, absolute extrema means max or min points in the given interval.
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
now to find min or max values, you take derivative of function and set it =0
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
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 ?
 one year ago

lilly21Best ResponseYou've already chosen the best response.1
or if its like 1/0 right?
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
in that case, we can find 'local' or 'absolute' values at the endpoints, they become min/max values.
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
i can't think of an example when u get 1/0 after taking the derivative.
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
here , you get f'(x) =2 we cannot equate this to 0
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
because 2 can never =0 hence there is no extrema, or as we say, no global extrema
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
but we can find absolute extrema, that is min/max in GIVEN INTERVAL
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
one of the endpoint is x=2 there what is f(x) = ?
 one year ago

hartnnBest ResponseYou've already chosen the best response.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
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
now put other end point, x=0 what is f(x)
 one year ago

lilly21Best ResponseYou've already chosen the best response.1
wait where did we get x=0?
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
thats where i got x=2 also earlier
 one year ago

lilly21Best ResponseYou've already chosen the best response.1
ooooooooo okay there will be 3 extrema right???
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
how come 3 ? one for x=2, and one for x=0
 one year ago

lilly21Best ResponseYou've already chosen the best response.1
we do the same for 0 right ???? plug it into the orig equation? right?
 one year ago

jaersynBest ResponseYou've already chosen the best response.0
you could just say there's no global min/max since the function is linear right?..
 one year ago

jaersynBest ResponseYou've already chosen the best response.0
k, thanks. double checking.
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
now put other end point, x=0 what is f(x)
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
so the other point is ?
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
and which one should be min and which one should be max ?
 one year ago

lilly21Best ResponseYou've already chosen the best response.1
0,3 is min the other is max?
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
yes, thats correct. clear with every step ?
 one year ago
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