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Calculus

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If f(x)=[x−1/(1+5 x)], there are two points on the graph of
y=f(x) at which the tangent lines are parallel to the line x−2y=2.
Type in the x values of
these points. Type the smaller number first, then the larger number.

  • Calculus -

    f(x) = x - 1/(1+5x)
    = x - (1+5x)^-1

    f'(x) = 1 + (1+5x)^-2 (5)
    = 1 + 5/(1+5x)^2

    the slope of x-2y=2 is 1/2

    so
    1 + 5/(1+5x)^2 = 1/2
    5/(1+5x)^2 = -1/2
    (1+5x)^2 = -10

    A square of something cannot be negative, so
    either there is no solution or you made an error in typing.
    Was the equation perhaps
    f(x) = (x-1)/(1+5x) ?

  • Calculus -

    yeah that's what I meant

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