1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    Science Advisor
    Homework Helper

    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


    User Avatar
    Science Advisor

    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


    User Avatar
    Science Advisor
    Homework Helper

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook