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Math Help - Finding the vaue of c given an equation of line

  1. #1
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    Finding the vaue of c given an equation of line

    Find the value of c such that the line y=5/6x+15/2 is tangent to the curve y= c(sqrt x)
    I am not sure where to start please help
    list after with finding the derivative of c(sqrt x)
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  2. #2
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    Re: Finding the vaue of c given an equation of line

    Hey mathisfun26.

    Hint: Start off by calculating the derivative (and noting that a tangent line has the form y = mx + b where m is the derivative).
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    Re: Finding the vaue of c given an equation of line

    Quote Originally Posted by mathisfun26 View Post
    Find the value of c such that the line y=5/6x+15/2 is tangent to the curve y= c(sqrt x)
    I am not sure where to start please help
    list after with finding the derivative of c(sqrt x)
    f(x)=c\sqrt{x}

    f^\prime(x)=\frac{c}{2\sqrt{x}}

    If t(x)=\tfrac{5}{6}x + \tfrac{15}{2} is tangent to f(x), then the slope of the line tangent to f(x) is \tfrac{5}{6}.

    To find the point at which t(x) is tangent to f(x), we first solve for x (in terms of c) in \tfrac{c}{2\sqrt{x}}= \tfrac{5}{6}. Plug this x-coordinate, which we label x_0, into f(x) to determine the y-coordinate of the point at which t(x) is tangent to f(x), which we call y_0.

    Finally, plug the point (x_0, y_0) into t(x) and you then should be able to solve for c.
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