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Math Help - question about points of inflection derivatives

  1. #1
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    question about points of inflection derivatives (urgent)

    y= 1/3 x^3 + x^2-15x +3

    y'= x^2 +2x-15 =0
    (x+5) (x-3)
    x=-5 x=3

    y'' = 2x +2 =0
    check for max or min
    2(-5)+2 =-8< 0 local max
    2(3) +2= 8 >o local min

    check for poi

    y'''= 2 not= 0 so we have a poi check if its stationary

    2x+2=0 2X=-2 x=- 2/2 x=-1

    non stationary point of infecton

    so if the was x=0 we have a stationary point of inflection?
    because i the book is they have this

    y=(x+4)^3
    y'=3(x+4)^2 =o x=-4
    y''= 6(x+4)=0 x=-4
    y'''=6 is not = to 0 we have a poi
    the order of the derivative is an odd number so at x=-4 we have a poi since y=0 when x=-1 the point is stationary

    bit confused because i thought that when the 2nd derviative result is calculated and x=0 then it is stationary when its x not = 0 nonstationary.
    Last edited by matlondon; April 11th 2010 at 04:00 AM.
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  2. #2
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    really need help on this
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  3. #3
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    Quote Originally Posted by matlondon View Post
    y= 1/3 x^3 + x^2-15x +3

    y'= x^2 +2x-15 =0
    (x+5) (x-3)
    x=-5 x=3

    y'' = 2x +2 =0
    check for max or min
    2(-5)+2 =-8< 0 local max
    2(3) +2= 8 >o local min

    check for poi

    y'''= 2 not= 0 so we have a poi check if its stationary

    2x+2=0 2X=-2 x=- 2/2 x=-1

    non stationary point of infecton

    so if the was x=0 we have a stationary point of inflection?
    because i the book is they have this

    y=(x+4)^3
    y'=3(x+4)^2 =o x=-4
    y''= 6(x+4)=0 x=-4
    y'''=6 is not = to 0 we have a poi
    the order of the derivative is an odd number so at x=-4 we have a poi since y=0 when x=-1 the point is stationary

    bit confused because i thought that when the 2nd derviative result is calculated and x=0 then it is stationary when its x not = 0 nonstationary.
    Hi matlondon,

    f(x)=(x+4)^3

    f'(x)=3(x+4)^2=0\ for\ x=-4

    f''(x)=6(x+4)=0\ for\ x=-4

    f''(x) is neither positive or negative at x=-4, so it is a saddle point, a stationary point of inflexion.

    That's as far as you need to go to know the difference.


    f(x)=\frac{x^3}{3}+x^2-15x+3

    f'(x)=x^2+2x-15=(x+5)(x-3)

    This is zero at x=-5,\ x=3

    f''(x)=2x+2=max\ at\ x=-5,\ min\ at\ x=3

    f''(x)=0\ for\ x=-1

    There is a non-stationary point of inflexion at x=-1
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  4. #4
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    f ' ' ' = 2 not equal to 0 so we have a poi
    not we plug in the x-1 into the first derivative to see if it stationary or non.

    f'(x)=-1^2+2(-1)-15= -18 this is non stationary

    so if the same the equation and the answer was zero then it would a a stationary poi?
    Last edited by matlondon; April 11th 2010 at 06:30 AM.
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  5. #5
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    stationary point

    Stationary points only when the first derivative =0
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  6. #6
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    Quote Originally Posted by matlondon View Post





    f ' ' ' = 2 not equal to 0 so we have a poi
    not we plug in the x-1 into the first derivative to see if it stationary or non.

    f'(x)=-1^2+2(-1)-15= -18 this is non stationary

    so if the same the equation and the answer was zero then it would a a stationary poi?
    Hi matlondon,

    no need to check the third derivative,
    that's a different ball game.

    If a point of inflexion is stationary, then the first and second derivatives are zero for the same x.

    Calculate the first derivative.
    This is zero at a maximum or minimum or saddle point.
    The saddle point is another term for a stationary point of inflexion.

    To know whether the point is a max, min or stationary point of inflexion,
    use the value of x that causes the first derivative to be zero.

    Plug this x into the 2nd derivative equation.

    If the answer is negative, the point is a local maximum.
    If the answer is positive, then it's a local minimum.
    if the answer is zero, it's a stationary point of inflexion.

    This applies to functions of a single variable, such as x.
    It's more complex for functions of more than one variable.
    Last edited by Archie Meade; April 11th 2010 at 02:01 PM. Reason: typo
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