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Math Help - Need some help drawing a graph

  1. #1
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    Need some help drawing a graph

    I need to draw a graph with this information :


    Graph a function on the interval [-2,5] with these characteristics:
    relative max at x = -1
    critical number at 0, but no extrema
    absolute max at x = 2
    absolute min at x = 5



    how would i go about doing this and understanding this problem?
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  2. #2
    Senior Member apcalculus's Avatar
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    Quote Originally Posted by AMaccy View Post
    I need to draw a graph with this information :
    Graph a function on the interval [-2,5] with these characteristics:
    relative max at x = -1
    critical number at 0, but no extrema
    absolute max at x = 2
    absolute min at x = 5
    how would i go about doing this and understanding this problem?
    Set f(2) = 6 to be the absolute max.
    Set f(5) = 0 to be the absolute min.

    Start with f(-2) = 1 in concave down and increasing through f(-1) = 3. From x= -1 to x = 0 the graph can be concave down and decreasing. (Make sure at x=-1 you have a horizontal tangent.) At x = 0, the graph changes concavity from up down to up but keeps decreasing, so make sure at x=0 the graph has a vertical tangent (critical number, since the first derivative is undefined).

    If you want the function to be continuous you may need to allow for another critical number. Otherwise, draw a vertical tangent somewhere between x=0 and x = 2, and ensure that x=2 is the 'highest' point. and x=5 is the 'lowest' point. I hope this helps.
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