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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 ;(1,1/5)

m =??
y =??

  • math -

    dy/dx = slope = [ (x+4)(2x) - x^2 ] /(x+4)^2

    = ( x^2 + 8 x ] / (x+4)^2

    at x = 1 this slope is
    = 9/25 so that is m

    goes through (1, 1/5)
    1/5 = (9/25)(1) + b
    5/25 = 9/25 + b
    b = -4/25
    so
    y = 9 x/25 - 4/25
    or
    25 y = 9 x - 4

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