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Find the slope m and an equation of the tangent line to the graph of the function f at the specified point.

f(x)=x^2/x+4 ; (3,9/7)

  • math -

    f ' (x) = ((x+4)(2x) - 2x(1) )/(x+4)^2
    = (2x^2 + 6x)/(x+4)^2
    when x = 3
    slope = 36/49

    so y = (36/49)x + b
    at (3,9/7)
    9/7 = (36/49)(3) + b
    b = 9/7 - 108/49
    = -45/49

    y = (36/49)x - 45/49 or (36x - 45)/49

    check my arithmetic

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