calculus

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Consider the function y=x/(x+1)

a) Find dy/dx

b) Find the equation of the line tangent to the curve at x=-2

c) Find the equation of the line normal to the curve at x=1

  • calculus -

    dy/dx = [(x+1)1 -x(1) ] / (x+1)^2

    = 1/(x+1)^2

    at x = -2
    y = -2/-1 = 2 so through point (-2,2)
    dy/dx = m = 1/1 = 1
    so
    y = 1 x + b
    2 = -2 + b
    b = 4
    y = x +
    for part c
    find a new m at x = 1, y = 1/2
    the m we want = -1/m
    then repeat method of part b

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