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Math Help - find gradient, equation, value, graph included.

  1. #1
    Junior Member
    Joined
    Oct 2007
    Posts
    32

    find gradient, equation, value, graph included.

    This seems simple but it doesnt really sink in for me.



    Can i have working out plz. thanx for any help
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  2. #2
    Junior Member
    Joined
    Sep 2007
    Posts
    30

    Solution

    I'm not sure about (i), but you don't need it to find the other two answers.

    ii. The slope of the tangent at a is given by dy/dx at a. So y'=2x, or, at a, y'=2a. We also know that the value of y(a) is a^2. Using point-slope form, the equation of the tangent is given by:

    (y-y_0)=m(x-x_0)
    or (y-a^2)=2a(x-a)

    iii. Plugging in the point (2,0) into the equation from (ii), we get

    (0-a^2)=2a(2-a)

    Then:
    -a^2=4a-2a^2
    0=4a-a^2
    0=-a(a-4)
    a=[0,4]

    Since a > 2 by the graph, a must be equal to 4.
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