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The line y=2x + b is tangent to the graph y= sqrt x at the point P= (a,sqrt a). Find P and determine b

  • math -

    Recall that sqrt(x) = x^(1/2), so the slope of the graph at any point x is 1/(2*sqrt(x)).

    So, at point P, x=a, slope is 1/(2*sqrt(a)).

    So, the line is y=2x + b, meaning that the slope is 2. That means that 2 = 1/(2*sqrt(a)). So, a=1/16.

    P = (1/16, 1/4)

    1/4 = 2(1/16)+b
    1/4 = 1/8 + b
    1/8 = b

    y = 2x + 1/8

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