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Math Help - Sketching graphs

  1. #1
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    Sketching graphs

    Just wondering if I could get a hand with sketching a graph where you aren't given the function. These are the details that are given -: f(0)=-1 f'(0)=0. f'(2)=0 f'(x) <0 for x <2. f'(x) >0 for 0<x<2. f'(x) <0 for x>2. Any help with finding critical points would be appreciated cheers
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  2. #2
    Junior Member Bradyns's Avatar
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    Re: Sketching graphs

    f'(0)=0 f(0) = -1,
    The gradient at x=0 is zero.

    f'(2)=0
    at x=2, the gradient is zero.

    f'(x)<0 for x<2.
    The gradient is less than zero for any value strictly less than x=2.

    f'(x)<0 for x>2
    The gradient is less than zero for any value strictly greater than x=2.

    f'(x)>0 for 0<x<2.
    The gradient is greater than zero for any values between (0, 2).

    This seems to be a very disjointed graph.
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  3. #3
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    Re: Sketching graphs

    Hello, Wattsy!

    Just wondering if I could get a hand with sketching a graph where you aren't given the function.

    These are the details that are given:
    . . f(0) = \text{-}1\qquad f'(0) = 0 \qquad f'(2) = 0
    . . f'(x) < 0\,\text{ for }x < 2 \qquad f'(x) > 0\,\text{ for }0 < x < 2 \qquad f'(x) < 0\,\text{ for }x > 2

    Any help with finding critical points would be appreciated.

    f(0) = \text{-}1
    . . The graph has y-intercept (0,\text{-}1)

    f'(0) = 0
    . . There is a horizontal tangent at (0,\text{-}1)

    f'(2) = 0
    . . There is a horizontal tangent at \left(2,f(2)\right)

    f'(x) < 0 \,\text{ for }x < 2
    . . The graph is decreasing on (\text{-}\infty,2)

    f'(x) > 0\,\text{ for }0 < x < 2
    . . The graph is increasing on (0,2)

    f'(x) < 0\,\text{ for }x > 2
    . . The graph is decreasing on (2,\infty)


    The graph seems to be a cubic function . . .

    Code:
                  |
        *         |
                  |
                  |
                  |               Q
         *        |           - - o - -
                  |           *   :   *
                  |         *     :     *
          *       |        *      :      *
                  |       *       :
    . . ---*------+------*--------+-------*---
            *     |     *         2
              * -1|   *            
              - - o - -                    *
                  |P
                  |
                  |
                  |                         *
                  |
    There is a relative minimum at P(0,\text{-}1).

    There is a relative maximum at Q\!:\:x = 2.
    But we don't know the y-value of point Q.
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