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Finding Values of a Function (increasing, decreasing, IPs, etc.)

  1. Nov 18, 2007 #1
    So the function is [tex]f(x) = 2 + 3x^{2} - x^{4}[/tex]

    Find the intervals of increase + decrease, local max + min value, inflection points (IP), interval the function is concave up + down

    I know that I need to first find f'(x) to find the increase and decrease, so I solved that:

    [tex]f'(x) = 6x - 4x^{3}[/tex]

    Now, the problem I'm having is finding the critical numbers. I know that 0 is obviously one of them, but I don't know what the other one is (since I'm quite confident that there is another one)
    Thanks for your help!
     
  2. jcsd
  3. Nov 18, 2007 #2
    1. set your derivative equal to 0 and solve for x
     
  4. Nov 18, 2007 #3

    HallsofIvy

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    I think that's what he said he did!

    Yes, momogiri, f'(x)= 6x- 4x3= x(6- 4x2)= 0 at the critical points. It is because of that "x" factor that x= 0 is one. The other two, of course, satisfy 6- 4x2= 0. Can you solve that?
     
  5. Nov 18, 2007 #4
    Oh gosh, I can't believe I didn't see that XD
    I'm pretty sure I can do it, Thanks for the help :D
     
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