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Math Help - Line Tangent to Two Parabolas

  1. #1
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    Line Tangent to Two Parabolas

    The region r, is bounded by the graphs of f(x)=x^2-3, g(x)=(x-3)^2, and the line T. T is tangent to the graph of f at the point (a,a^2-3) and tangent to the graph of g at the point (b,(b-3)^2).

    A) Show that a=b-3
    B) Find the numerical value of a and b
    C) write an equation of the line T
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  2. #2
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    Quote Originally Posted by rawkstar View Post
    The region r, is bounded by the graphs of f(x)=x^2-3, g(x)=(x-3)^2, and the line T. T is tangent to the graph of f at the point (a,a^2-3) and tangent to the graph of g at the point (b,(b-3)^2).

    A) Show that a=b-3


    \color{red}\mbox{Since slope of T at first point = slope of T at 2nd one, you get } \,f'(a)=g'(b)


    B) Find the numerical value of a and b

    \color{red}\mbox{Find tangent line at 1st, 2nd points , compare both equations: they're the same!}

    Tonio

    C) write an equation of the line T
    .
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