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Critical numbers

  1. May 1, 2007 #1
    how do you find critical numbers, and do you have to keep on plugging in a number until you find zero or is their an easier way
     
  2. jcsd
  3. May 1, 2007 #2
    i know the theorem already
     
  4. May 1, 2007 #3

    hage567

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    Homework Helper

    What theorem are you referring to?

    You take the derivative of the function, set it equal to zero, and solve.
     
  5. May 2, 2007 #4
    usually we take derivative of function and set it equal to 0 like hage567 said
    for example you consider this function
    y=x.x+x=x(2)+x
    y'=dy/dx
    y'=2x+1
    for finding the critical number we set it to zero
    y'=0
    => 2x+1=0
    => 2x=-1
    => x=-1/2
    -1/2 is critical number for this function
    and one of its usage is for finding the MAX. and MIN. of a function.
     
  6. May 2, 2007 #5
    Aren't points of inflection also critical points?
     
  7. May 2, 2007 #6

    HallsofIvy

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    Staff Emeritus
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    No. Critical points are where either the derivative is 0 or where the derivative does not exist. Points of inflection are where the secondderivative changes sign. That has to be where the second derivative is 0 or does not exist although not all such points are inflection points.

    For example, if f(x)= x3- 3x, then df/dx= 3x2- 3 so the critical points are x= 1 while d2f/dx2= 6x. The only inflection point is at x= 0.
     
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