Calculus AB

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Analyze the function ln x=cx^2 to find the unique value of c such that there is exactly one solution to the equation. To do this find the value of c such that both sides of the equation have equivalent slopes at some point; this will give you a proper x-coordinate to work with.

  • Calculus AB -

    following their suggested procedure, ...

    slope of lnx = 1/x
    slope of xc^2 = 2cx

    1/x = 2cx
    c = 1/(2x^2)

    then lnx = (1/(2x^2))x^2 = 1/2
    x = e^(1/2)
    x = √e

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