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Math Help - Need help sketching a graph

  1. #1
    bmh
    bmh is offline
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    Need help sketching a graph

    Please help me sketch this graph:
    f ' (x) > 0 when x<2 and when 2< x <5
    f ' (x) < 0 when x > 5
    f ' (2) = 0
    f " (x) < 0 when x < 2 and 4 < x < 7
    f " (x) > 0 when 2 < x < 4 and x > 7
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  2. #2
    MHF Contributor
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    Just one piece at a time.

    f ' (x) > 0 when x < 2

    Up from the left.

    f ' (2) = 0

    Level off at x = 2

    f ' (x) > 0 when 2 < x < 5

    Surprise! Don't trun around and start down at x = 2. (Think about y\;=\;x^{3} at the Origin)

    f ' (x) < 0 when x > 5

    Okay, NOW turn around and start down. Notice, however, that there must be a point of inflection between x=2 and x=5.

    f " (x) < 0 when x < 2 and 4 < x < 7
    f " (x) > 0 when 2 < x < 4 and x > 7

    Aw! They gave away the point of inflection at x = 4. Further, they gave us another one at x = 7, so don't be wandering off the the bottom of the world.
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