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    differentiation question

    For what values of a and b is the line 2x+y=b tangent to the parabola y=ax^2 when x=2
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    Quote Originally Posted by cityismine View Post
    For what values of a and b is the line 2x+y=b tangent to the parabola y=ax^2 when x=2

    When x = 2, y = 4a.

    y' = 2ax = 4a

    y - 4a = y'(x - 2) = 4a(x - 2) \Rightarrow y - 4a = 4ax - 8a \Rightarrow y = 4ax - 4a

    Comparing y = 4ax - 4a and 2x + y = b,

    Writing it: -4a = -4ax + y makes it easy.

    2 = -4a = b \Rightarrow a = -\frac{1}{2} , b = 2
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