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Math Help - Tangent equation

  1. #1
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    Tangent equation

    My aim is to compose a tangent equation for the line y=(x-1)*(x+1)*(x+2) provided that tangent points are intersections with x-axis.
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  2. #2
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    Quote Originally Posted by totalnewbie
    My aim is to compose a tangent equation for the line y=(x-1)*(x+1)*(x+2) provided that tangent points are intersections with x-axis.
    Hello,

    you know already the intersections between x-axis and curve:
    (-2,0), (-1,0), (1,0).

    Now you need the slope of the tangent lines:

    Your function is y=f(x)=(x-1)(x+1)(x+2)=x^3+2x^2-x-2

    The gradient of the function gives the slope of the tangents:

    f'(x)=3x^2+4x-1

    First slope: m_1=f'(-2)=3 \cdot 4 +4 \cdot(-2) - 1=3
    2nd slope: m_2=f'(-1)=3 \cdot 1 +4 \cdot(-1) - 1=-2
    3rd slope: m_3=f'(1)=3 \cdot 1 +4 \cdot(1) - 1=6

    Now use the point-slope-formula and you'll get:
    t_1:y=3 \cdot (x+2)
    t_2:y=-2 \cdot (x+1)
    t_3:y=6 \cdot (x-1)

    Greetings

    EB
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