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Math Help - Inflection Point

  1. #1
    Junior Member
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    Inflection Point

    How would you find the inflection point for the following problem:

    NOTE: I worked out most of this problem, it gives you the initial function and then asks you to do the following things:
    (a)Find the intervals of increase and decrease.
    (b)Find local maximum and minimum values.
    (c)Find the interval of concavity and the inflection points.
    (d)Use the information from (a)-(c) to sketch the graph.
    -I did everything except find the inflection points and sketch the graph.-

    h(x)=x^5-2x^3+x
    h'(x)=5x^4-6x^2+1
    h''(x)=20x^2-12x

    H is increasing on: [-(infinity), 1/5] and [1,(infinity)]
    H is decreasing on: [1/5, 1]

    Local max at:
    -1: h'(-1)=0
    -1/5: h'(-1/5)=-.18432....
    1/5: h'(1/5)=.18432

    Local min at:
    1: h'(1) = 0

    h is concave up on intervals [-.77,0], [.77, (infinity)]
    h is concave down on intervals [-(infinity), -.77], [0,.77]

    ---------------------------

    Let me know if you need any more information or if I made a mistake somewhere along the way.
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  2. #2
    sss
    sss is offline
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    For getting inflection points solve f''(x)=0

    20x^3-12x=0
    x(20x^2-12)=0
    x=0,sqrt(3/5),-sqrt(3/5)
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