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HELP (inflection points and whatnot)

  1. Dec 14, 2009 #1
    HELP!!! (inflection points and whatnot)

    Okay I know how to differentiate but I suck at simplifying the equation

    For example

    f''(x) = (x^2 + 3)^2(-12)-(-12x)(2)(x^2+3)(2x)
    ^Second derivative

    all over

    (x^2+4)^4

    Now the answer is 36(x^2-1) over (x^2+3)^3

    But as to how they came up with 36(x^2-1) is beyond me, I tried breaking up the numerator and solving one half of the equation and the other half; breaking it down piece by piece, but I came up with an equation that resembled nothing like I was suppose to get.

    The next question I have is finding the absolute max and min of f(x)= sq root of 81-x^2 in the interval (-9,9)

    it says that it's (NONE, NONE) for an abs min and (0,9) for an abs max

    then they want me to get it on an interval of [4.5,9) which leads to (NONE,NONE) for the abs min and (4.5, 7.89) for a max. How does that work?

    As for the trig problems...I don't even know how to go about those...f(x)=8x+sin(x)

    I know the derivative of this is f'(x)=8+cos(x) but finding the open intervals where the function is increasing/decreasing as well as applying the first derivative test to find the relative extrema is something I don't know how to go about doing...maybe I'm making it a little complicated...

    I don't know how to find the concavity/points of inflection of f(x)=4csc(5x/2) on the interval (0,2pi) or how to find it with this function f(x)=8sin(x)+4cos(x)
     
  2. jcsd
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