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Differentiating modulus

  1. Jun 10, 2010 #1
    Ok so i was wondering if what i am doing is correct, But it gets the wrong minimum point?
    So my function is y=|x+4|

    1) y^2=x+4
    3)dy/dx = 1/2y
    4)dy/dx = 1/2|x+4|

    I set that 0 and get

    Am i write in thinking this cannot be solved? or missing something?

  2. jcsd
  3. Jun 10, 2010 #2


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    Homework Helper

    Yep that's right. It's the same as asking what number x can be used to make 1/x=0? None of course. And at x=-4 the derivative is undefined.
  4. Jun 10, 2010 #3


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    It goes wrong from the start, [itex]y^2 \neq x+4[/itex].
  5. Jun 10, 2010 #4


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    Oh right, I guess I brushed over it too fast.

    When that mistake is fixed, you'll still find the the derivative cannot equal zero anywhere and it's still undefined at x=-4 with the form 0/0
  6. Jun 10, 2010 #5
    Oh yeah, thanks,
  7. Jun 10, 2010 #6


    Staff: Mentor

    Another approach is to get rid of the absolute values by writing the function as
    y = x + 4, x >= -4
    y = -(x + 4), x < -4

    Then y' = 1 for x > -4 and y' = -1 for x < - 4. y' does not exist at x = -4.

    Any extreme points of a function occur at places where y' = 0, or y' is undefined, or at finite endpoints of the domain in cases where a function is defined only on an interval [a, b].
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