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Math Help - finding the slope of a tangent line

  1. #1
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    finding the slope of a tangent line

    I have been stuck on this question for a while now. I need to find the slope of the tangent to the curve 5 over the square root of x (5/squarerootX)
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    Re: finding the slope of a tangent line

    start by rewriting y = \frac{5}{\sqrt{x}} so that you may use the power rule for derivatives

    y = 5x^{-1/2}

    continue ...
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    Re: finding the slope of a tangent line

    When I use the power rule I get (-5/2) (x^-3/2) if i did that right i am still going to have a radical so how will I find the slope?
    I'm sorry for coming off as such an amateur, but calc is the bane of my existence
    Last edited by neontiger94; September 16th 2012 at 12:19 PM.
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    Re: finding the slope of a tangent line

    Quote Originally Posted by neontiger94 View Post
    When I use the power rule I get (-5/2) (x^-3/2) if i did that right i am still going to have a radical so how will I find the slope?
    I'm sorry for coming off as such an amateur, but calc is the bane of my existence
    You don't. The tangent at \left(x_0,\frac{5}{\sqrt{x_0}}\right) is y-\frac{5}{\sqrt{x_0}}=\frac{-5}{2\sqrt{x_0^3}}(x-x_0)
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    Re: finding the slope of a tangent line

    Thats what I thought the answer was, but maybe I didnt specify the question properly. The question reads Find the slope m of the tangent to the curve
    y = 5/square root x


    at the point where x = a > 0.
    does this help at all, beacuse I think I'm supposed to find the exact slope using the derivative as a function
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    Re: finding the slope of a tangent line

    Quote Originally Posted by neontiger94 View Post
    Thats what I thought the answer was, but maybe I didnt specify the question properly. The question reads Find the slope m of the tangent to the curve
    y = 5/square root x at the point where x = a > 0.
    does this help at all, beacuse I think I'm supposed to find the exact slope using the derivative as a function
    Always post the complete problem.

    But that changes nothing in what I posted. Just let a=x_0 and you are done.
    Thanks from neontiger94
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  7. #7
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    Re: finding the slope of a tangent line

    Okay thank you I should have used the power rule from the beginning
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