Give an equation to the line tangent to f(x)=7/(3-2x) at x=6.?

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  • f(x) = 7 * (3 - 2x)^(-1)

    f'(x) = 7 * (-2) * (-1) * (3 - 2x)^(-2) = 14 / (3 - 2x)^2

    f(6) = 7 * (3 - 12)^(-1) = 7 * (-9)^(-1) = 7 * (-1/9) = -7/9

    f'(6) = 14 / (3 - 12)^2 = 14 / (-9)^2 = 14/81

    y - (-7/9) = (14/81) * (x - 6)

    y + (7/9) = (14x - 84) / 81

    81y + 63 = 14x - 84

    81y = 14x - 147

    y = (14x - 147) / 81

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