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Math Help - function of x help again

  1. #1
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    function of x help again

    i have the function f(x) = x^2+3(x)/2(x)^2+6(x)+4. I need to calculate the intervals on which f is increasing or decreasing, the nature of any stationary points and the value of f at each of these points. I also need to work out the asymptotic behaviour of f. I dont know where to begin!!! Please can anyone help.
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  2. #2
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    What is the equation here?

    f(x)= x^2+\frac{3x}{2x^2}+6x+4
    or

    f(x)= \frac{x^2+3x}{2x^2+6x+4}
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  3. #3
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    Its the bottom equation
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  4. #4
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    Ok, first thing to do is factorise the denominator.

    What do you get?
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  5. #5
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    so far I have factorised the denominator of f(x) to (2x+4)(x+1) giving x =-1 and x = -2. Which gave me intervals of (-infinity,-2) where f is positive, (-2,-1) where f is negative and (-1,infinity) where f is positive.

    I determined that the function was neither od or even as no features were symmetrical.

    Found the y intercept to be 0 and the x-intercepts to be 0 and -3

    and now Im at a stand still and dont know what to do next?
    Last edited by reallystickiam; February 9th 2011 at 02:38 PM. Reason: more information
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  6. #6
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    Sounds good, you need to find where the function is increasing/decreasing so take the derivative using the quoient rule.

    What do you get?
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