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Math Help - Integration

  1. #1
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    Integration

    Hi I am slightly stuck with what to do for this question. Any help would be great.

    curve: y= x(x-1)(x-2)

    a) find the equation of the tangent at the point P whose x coordinate is 1/2

    b) show that the point Q(2,0) lies on the tangent and on C

    c) Find the shaded area

    Thanks
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  2. #2
    o_O
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    1. Remember. The derivative of a function at a particular point represents the slope. So find y' and plug in x = 1/2 to get your slope. Then, use the point slope form of a line to get your tangent line: y - y_{0} = m(x - x_{0}) where (x_{0}, y_{0}) is your point P.

    2. Plug in Q(2,0) into your tangent line equation to see if there is an equality. Do the same for C.

    3. What shaded area?
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  3. #3
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by soso View Post
    Hi I am slightly stuck with what to do for this question. Any help would be great.

    curve: y= x(x-1)(x-2)

    a) find the equation of the tangent at the point P whose x coordinate is 1/2

    b) show that the point Q(2,0) lies on the tangent and on C

    c) Find the shaded area

    Thanks
    If you mean the area bounded by the curve and the x-axis...we see the curve equals 0 at x=0. x=1, x=2...then the area of the region would be \int_0^{2}|x(x-1)(x-2)|dx
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