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Math Help - Derivative Function Solve for a,b,c Problem

  1. #1
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    Derivative Function Solve for a,b,c Problem

    Here's a Mind Teaser for everyone that certainly is teasing me right now..


    Let f be the function that is given by f(x)= ax+b/x2-c and that has the following properties:

    1. The graph of f is symmetric with respect to the y-axis (meaning f(x)=f(-x)?)

    2. Lim x→3 f(x)= -∞

    3. f'(-2)= -4


    a.) Determine the values of a,b, and c.
    b.) Write an equation for each vertical and each horizontal asymptote of the graph f.


    ATTEMPT:
    So I determine that a must equal 0 because if the graph is symettric about the y-axis, that means (x) must equal (-x). I solved for a, and got a=-a, where a=0.

    Then I get lost. Where would I go from there?
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  2. #2
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    Please be more precise when typing your function...

    Is it f(x) = \frac{ax+b}{x^2-c}? or \frac{ax+b}{x^2}-c?
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  3. #3
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    It is your first choice. All over (x^2-c).
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  4. #4
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    Quote Originally Posted by r2d2 View Post
    It is your first choice. All over (x^2-c).
    OK then. a=0 is correct, so we have f(x) = \frac{b}{x^2-c}...

    First, think what could cause \lim_{x\to3}f(x) = -\infty? One part of the function has to go "wild" -- could it be the numerator? or the denominator? and why?

    Second, find the derivative and substitute the given value to find the last constant.
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  5. #5
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    Ok. It actually says the limit as x approaches 3 from the left. Would that mean the denominator would go to 0, meaning that c would be 9?
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  6. #6
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    Quote Originally Posted by r2d2 View Post
    Ok. It actually says the limit as x approaches 3 from the left. Would that mean the denominator would go to 0, meaning that c would be 9?
    Yes, that is correct. Can you find b now?
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  7. #7
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    it seems that b would have to equal 9 so the function be equal to 0. Would that be correct?
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  8. #8
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    Quote Originally Posted by r2d2 View Post
    it seems that b would have to equal 9 so the function be equal to 0. Would that be correct?
    It says nowhere that the function needs to equal 0. You need to find the derivative and solve f'(-2)=-4 with regards to b.
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