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Math Help - Finding the graph of a function with only derivative and domain.

  1. #1
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    Finding the graph of a function with only derivative and domain.

    Finding the graph of a function with only derivative and domain.-math.png
    "The graph below is the graph of f', the derivative of f; The domain of the derivative -5≤x≤6"

    1) The critical points for f are x=
    2) The critical points for f' are x= -3, -2/3, 2, 4, 5.
    3) F has a local maximum when x=
    4) F has its maximum value on [-5,6] when x=
    ...
    Is this information obtainable without knowing the original function or graphing the original function?
    I would assume it is, but I'm not sure how to go about it?
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    MHF Contributor MarkFL's Avatar
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    Re: Finding the graph of a function with only derivative and domain.

    1.) The critical points for f are where f' has its roots.

    3.) f will have a local maximum where f' goes from positive to negative.

    4.) Think about the integral of f', which is f. Is the area above the x-axis greater than the area below it to the left?
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    Re: Finding the graph of a function with only derivative and domain.

    Thanks MarkFL2
    I'm still stuck on the questions asking about coords.

    4 as listed before.
    10) Does f' have a minimum value on [-5,6]? Explain. (it doesnt look like it does?)
    11) Does f'' have a miniumum value on [-5,6]? Explain. (it would have a maximum if anything)

    The graph shows at -5,6 that it would go infinity to the left, wouldn't that stop any chance of a minimum being at that point?
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    MHF Contributor MarkFL's Avatar
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    Re: Finding the graph of a function with only derivative and domain.

    4.) Which looks greater, the amount of decrease of f from x = -5 to 1 or the amount of increase from x = 1 to 3? This indicates that f must have an absolute maximum where?

    10.) It appears the absolute minimum for f' on the given interval is at x = -2/3.

    11.) Is there a place where the slope of f' is a minimum?
    Last edited by MarkFL; November 1st 2012 at 12:19 AM.
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    Re: Finding the graph of a function with only derivative and domain.

    Oh. I was thinking [-5,6] was an x and y coord.


    4) x = 2
    10) Yes, at x=-2/3 the graph of f' goes from decreasing to increasing showing there is a minimum.
    11) Yes, at x= -2 the slope of f' changes from decreasing to increasing showing there is a minimum.

    Does this look correct?
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    Re: Finding the graph of a function with only derivative and domain.

    Also to just check.

    Question 8) f' has its maximum value when x= ( I put -3, and 2). Where the slopes reach 0 while being concave down. Would this be correct? It threw me off because the question asks for 1 x value.
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    MHF Contributor MarkFL's Avatar
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    Re: Finding the graph of a function with only derivative and domain.

    Just look at the graph, and find where the absolute maximum of f' occurs, since the graph is of f'.
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