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Math Help - critical values

  1. #1
    Junior Member
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    Sep 2007
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    critical values

    Hi guys, I was given a graph of the derivative or f ' (x), not f (x), which is where I am slightly confused on this problem... Given the graph of f '(x) answer questions about f(x)




    a) for what values of x is the original function increasing/decreasing?
    b) what values does original function, f(x) have horiz tangent lines?
    c) what approx values of x does original function, f(x) have inflection points?

    Here's what I have so far, but im not sure if I am doing this correctly for the values of the original function or for the graph of the derivative:
    increasing at -infinity to -1.5 AND 1 To infinity
    decreasing at -1.5 to 1
    Horiz tangent lines at x=1 and -1.5
    Inflection Points = none
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  2. #2
    MHF Contributor
    Joined
    Apr 2005
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    So the graph shown is for the 1st derivative of f(x).

    The function f(x) increasing if the 1st derivative is positive.
    So, that is in the intervals (-2,-1) and (2, +infinity)
    Or, from just after x = -2 to just before x = -1, and then, from just after x = 2 to positive infinity.

    The function f(x) is decreasing if the 1st derivative is negative.
    So that is from negative infinity to just before x = -2, then from just after x = -1 to just before x = 2.

    f(x) has horizontal tangent lines where the 1st derivative is zero.
    So those are at x = -2, x = -1 and x = 2.

    f(x) has an inflection point where its 1st derivative is at maximum or minimum.
    So those are at x = -1.5 and x = 1, if my eyes can see clearly.
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  3. #3
    Junior Member
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    Sep 2007
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    thx ticbol, perfect explanation!
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