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Setting Derivative = 0 and solving

  1. Oct 17, 2013 #1
    1. The problem statement, all variables and given/known data
    I'm currently working on a problem that requires me to set the derivative = 0 and solve for a variable (call it x). The derivative comes out to be a fraction, with x terms in both the numerator and denominator. Is it legal to just multiply 0 by the denominator (thereby canceling it) even if it has the term of interest as part of it?

    Simple Ex: say the derivative came out to be x-3 / 2x. And I want to solve for x.
    When I set that derivative equal to zero, can i just multiply 0 by 2x, leaving x-3=0? So x=3

    2. Relevant equations

    none

    3. The attempt at a solution
    ...
     
  2. jcsd
  3. Oct 17, 2013 #2

    rcgldr

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    That should be ok. You could also divide the left side by x / x, assuming that x is not equal to zero, resulting in:

    ( 1 - (3/x) ) / 2 = 0
     
  4. Oct 17, 2013 #3
    thank you
     
  5. Oct 17, 2013 #4
    i thought they're supposed to show the work?
     
  6. Oct 17, 2013 #5
    It is a requirement for HW problems, but my question was geared towards a concept. The equation I'm deriving for the HW would probably take up an entire line on here. The example I put on was just that, an example, it wasn't even close to my actual problem (although I wish it was haha)
     
  7. Oct 17, 2013 #6

    rcgldr

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    Multiplying both sides by 2x is just as valid as dividing the left side by x/x. I only showed that as an alternative in case there's a situation where that would be a better option for a different equation.
     
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