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anonymous
 5 years ago
Give an example of a function, g(x), that has a local maximum
at (3; 3) and a local minimum at (3, 3).
anonymous
 5 years ago
Give an example of a function, g(x), that has a local maximum at (3; 3) and a local minimum at (3, 3).

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amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0its a cubic at its basic

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0centered at the the origin

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0g'(3) = 0 and g'(3) = 0

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0x^3 derived is 3x^2 3(3)^2 = 0 27 = 0 27  27 = 0

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.03x^2  27 = g' x^3  27x +C = function of g(x); just gotta calibrate for (3,3)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.03 = (3)^3 27(3) + C 3 17 + 27(3) = C C = 61 g(x) = x^2 27x + 61 perhaps?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0g(x) = x^3 27x + 61 that is lol

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Thanks a lot. I really appreciate it.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0it might be wrong; i havent checked it good wnough yet :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Hmm, when I graph it it the maximum and minimum isn't (3, 3) and (3, 3) let me try with C=51

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0i see it too; :) gotta figure out where I looked at it wrong

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0g' = 3x^2  27 = 0 at 3 and 3 so the derivative is good

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0g(x) = x^3  27x + C if we integrate it...

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0(x=3,y=3) should fit it and (x=3,y=3) should fit it, so we solve for C with these parameters

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.03 = (3)^3  27(3) + C and 3 = (3)^3  27(3) + C 3  (3)^3 + 27(3) = C OR 3  (3)^3 + 27(3) = C

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0C = 51 or C = 51 which doesnt work out to well in teh end

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0g(0) would also have to equal 0

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I just graphed it again and the minimum is at (3, 3) but not the Maximum

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the maximum is not at (3, 3)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0g(x) = x^3  27x ... thats it

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0ack!!... that aint it either.. lol

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Haha, it's ok, thanks a lot for the help though. But I got a little help from someone but have no idea how hey got it, maybe you can help elaborate this. For this problem they started from this: (x+3)(x3) g'(x)= X^2 9 = 1/3x^3 9 ???? Have no idea as to how they got here for this problem.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0i got some idea, but have to look at it some more

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0g'(x) has roots at 3 and 3 so g'(x) = x^2  9 if we combine them; which is good; then integrate up to x^3   9x tho 3

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0(1/3)(x^3)  9x + C is the family of curves for it....

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0C = 15 then i think (1/3)x^3  9x 15 ; lets check it

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Now the max is right but not the min...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I did this very quickly; \(f(x)=x^327x51\). Check it!!

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0it works for one , but not the other

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0g(0) = 0 has to be part of te graph

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0so adding somethig to it aint gonna help; we gotta find the right 'slope'

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0M(x^3  Bx) is what we need

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0Dx(Mx^3  MBx) 3Mx^2  MB M(3x^2  B) = 0 when x = 3 or 3

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0Maybe include more powers of x?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0or derive again for inflection...

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.06Mx = 0 when x = 0 lol ... that dint work out to well

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0haha, thanks, i really appreciate the help

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0k(3)^3 = 3 27k = 3 k = 1/9 maybe? x^3  ; 3x^2/9 = x^2/3 i wonder 9
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