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calculus

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Find the number c if the line y=x is to be tangent to the graph of f(x)=x^4+c. what are the coordinates of the points of tangency?

  • calculus - ,

    so x = x^2 + c
    x^2 - x + c = 0 must have only one root, that is,
    the discriminant must be zero

    b^2 - 4ac = 0
    1 - 4(1)(c) = 0
    c = 1/4

    so x^2 -x + 1/4 = 0
    (x- 1/2)^2 = 0
    x = 1/2
    then y = 1/2

    the point is (1/2,1/2)

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