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Optimization

AP Calculus AB· difficulty 4/5

The point on y=xy = \sqrt{x} closest to (2,0)(2, 0) has x-coordinate

  • A

    22

  • B

    00

  • C

    11

  • D

    32\frac{3}{2}

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Explanation

Squared distance D=(x−2)2+xD = (x-2)^2 + x. D′=2(x−2)+1=0⇒x=3/2D' = 2(x-2) + 1 = 0 \Rightarrow x = 3/2.

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