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Picewise derivative problems

  1. Dec 4, 2008 #1
    1. The problem statement, all variables and given/known data
    y=|x^2-4|+2 find f`,relative extrema,minima.

    2. Relevant equations
    Detailed graphing of
    y={ 9-x,x<=3

    using derivatives

    3. The attempt at a solution
    I m not sure how to do this sort of prblems.
  2. jcsd
  3. Dec 5, 2008 #2


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    Usually, it works to get rid of the absolute value signs. So first solve where x^2 - 4 is positive and negative and treat those cases separately.

    Simple example: derive y = |x|.
    1) For x > 0 (or x = 0), this reads y = x. Then the derivative is y' = 1.
    2) For x < 0, it means y = -x. Then the derivative is y' = -1.

    Afterwards, you may try to find a general formula. For example, if you are used to working with such things, you might write something like: y' = sign(x) for x non-zero (and for x = 0, the derivative is undefined).
  4. Dec 5, 2008 #3


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    Graphing is the simplest thing to do. As CompuChip said, get rid of the absolute value signs. x2- 4 is 0 at x= -2 and x= 2. Between -2 and 2, x2- 4 is negative and so |x2- 4|= 4- x2. Graph y= x2- 4 up to x= -2, then y= 4- x2 for x between -2 and 2, and, finally, graph y= x2- 4 for x> 2.

    That is the same, of course, as graphing y= x2- 4, then "flipping" the part of the graph below the y-axis up. It should be easy to see where relative max and min are.
  5. Dec 5, 2008 #4


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    And for your real question, don't forget the +2 :smile:
  6. Dec 5, 2008 #5
    Thanks i have understood that.I know how to graph piecewise functions but i m confused how to draw them by using the method of derivative i mean by f` and f`` increasing part decreasing part,concave up down and so on.
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