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Given (f(x)=x^3-6x^2+15 : i did the problem but i have a feeling that is wrong. help.

  1. Dec 4, 2012 #1
    1. The problem statement, all variables and given/known data
    hey guys. please help me out i tried the problem but for some reason i feel like its wrong. thank you in advance.


    2. Relevant equations
    given f(x)=x^3-6x^2+15
    a)find the intervals of inc/dec
    b)find the local max/min if any
    c)find intervals of concavity
    d)find the inflection points if any
    e)use the information to sketch the graph


    3. The attempt at a solution

    f'(x)=3x^2-32x
    =x(3x-32)
    x=0 x=32/3 (critical points)

    from -infinity to 0 the function is positive
    from 0 to the function is negative
    from 32/3 to infinity the function is positive

    f(0) = 15 (0,15) = local min
    f(32/5) = 35.7 = local max

    f''(x)=6x-32
    =6x-32=0
    =16/3

    from -infinity to 16/3 the function is concave down
    from 16/3 to infinity the function is concave up

    point of inflection (16/3, 15)

    cant show the graph here
     
  2. jcsd
  3. Dec 4, 2012 #2

    Dick

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    Re: given (f(x)=x^3-6x^2+15 : i did the problem but i have a feeling that is wrong. h

    Your derivative is wrong. Try and fix that and try again. And whether the derivative is positive or negative tells you whether the function is increasing or decreasing, yes?
     
    Last edited: Dec 4, 2012
  4. Dec 4, 2012 #3
    Re: given (f(x)=x^3-6x^2+15 : i did the problem but i have a feeling that is wrong. h

    the first derivative is 3x^2-32x
    i factored it to x(3x-32). is that wrong?
     
  5. Dec 4, 2012 #4

    Ray Vickson

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    Re: given (f(x)=x^3-6x^2+15 : i did the problem but i have a feeling that is wrong. h

    The function f(x) =x^3-6x^2+15 is NOT positive on (-∞,0): when x is large and negative the x^3 term is swamps all the others and is < 0, so f(x) < 0.
     
  6. Dec 4, 2012 #5
    Re: given (f(x)=x^3-6x^2+15 : i did the problem but i have a feeling that is wrong. h

    i see where i did wrong there. thanks
     
  7. Dec 4, 2012 #6
    Re: given (f(x)=x^3-6x^2+15 : i did the problem but i have a feeling that is wrong. h

    i see where you say the deriv was wrong...
    the derive is 3x^2-12x :smile: sorry i didnt notice that i did that
     
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