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

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

infoshark
 3 years ago
Best ResponseYou've already chosen the best response.0what are the roots of 2 ? where does it cross the x axis

infoshark
 3 years ago
Best ResponseYou've already chosen the best response.0can y ever be zero if it always equals 2 ?

infoshark
 3 years ago
Best ResponseYou've already chosen the best response.0any max extrema then ?

lilly21
 3 years ago
Best ResponseYou've already chosen the best response.1im kinda of confused by ur question :[

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1u got x=2 put it in f(x) to find the extrema

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

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1i 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
 3 years ago
Best ResponseYou've already chosen the best response.1whenever we don't get global extrema, we put endpoints....remember this.

lilly21
 3 years ago
Best ResponseYou've already chosen the best response.1i am utterly confused :[

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1ok, absolute extrema means max or min points in the given interval.

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

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1then 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
 3 years ago
Best ResponseYou've already chosen the best response.1or if its like 1/0 right?

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

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1i can't think of an example when u get 1/0 after taking the derivative.

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1here , you get f'(x) =2 we cannot equate this to 0

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

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1but we can find absolute extrema, that is min/max in GIVEN INTERVAL

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

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1so the point is (2,1) and this is one of the extrema we don't know yet whether this is max or min

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1now put other end point, x=0 what is f(x)

lilly21
 3 years ago
Best ResponseYou've already chosen the best response.1wait where did we get x=0?

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1thats where i got x=2 also earlier

lilly21
 3 years ago
Best ResponseYou've already chosen the best response.1ooooooooo okay there will be 3 extrema right???

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

lilly21
 3 years ago
Best ResponseYou've already chosen the best response.1we do the same for 0 right ???? plug it into the orig equation? right?

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

jaersyn
 3 years ago
Best ResponseYou've already chosen the best response.0k, thanks. double checking.

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1now put other end point, x=0 what is f(x)

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1and which one should be min and which one should be max ?

lilly21
 3 years ago
Best ResponseYou've already chosen the best response.10,3 is min the other is max?

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1yes, thats correct. clear with every step ?
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