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    Line Equations : Tangents & Normals

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    I) Find the equation of the tangent to y=x(1-x) at x=1
    ii) Find the equation of the normal to y=x(1-x) at x=1
    iii) Find the equations of the tangents to y=x(1-x) that pass through (-1, 1/4)

    © BrainMass Inc. brainmass.com March 4, 2021, 5:53 pm ad1c9bdddf
    https://brainmass.com/math/calculus-and-analysis/line-equations-tangents-normals-16505

    Solution Preview

    i.)
    At x =1: y = 1*(1-1) = 0
    Hence, given point (x1, y1)= (1,0)

    dy/dx = y' = 1 - 2x
    y'|(at x = 1) = 1 - 2*1 = -1

    Hence, Eqn of tangent:
    y -y1 = y'(x-x1)
    => y - 0 = (-1)*(x-1)
    => x + y = 1 --Answer

    ii.)
    Eqn of normal:
    (x-x1) + y'(y-y1) = 0
    => (x-1) + (-1)*(y-0) = 0
    => x-1 -y = 0
    => x - y = 1 ...

    Solution Summary

    Tangents and normals are calculated.

    $2.49

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