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29 June, 10:25

For what values of a and b is the line 2x + y = b tangent to the parabola y = ax2 when x = 3?

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  1. 29 June, 13:52
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    Y=ax^2

    Differentiate both sides with respect to x, we have y'=2ax

    Put x=3, we have y'=6a

    Hence the slope of 2x+y=b is 6a, then a=-1/3

    y = (-1/3) (3^2) = - 3

    Put (3,-3) into the line,

    b=6-3

    Hence a=-1/3, b=3
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