a. How close does the curve $y = \sqrt{x}$ come to the point $(\frac{13}{2}, 0)$? (Hint If the square of the distance is minimized, square roots can be avoided.) b. Graph the distance function D(x) (the square of the distance) and $y = \sqrt{x}$ together and reconcile the result with the result in part (a).
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Since the curve is y=x, we can substitute x=0 into the equation to find the y-coordinate of the point on the curve closest to 0. When x=0, y=0. So the point on the curve closest to 0 is (0,0). b) To graph the distance function D(x) and y=x together, we need to Show more…
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\begin{equation} \begin{array}{l}{\text { a. How close does the curve } y=\sqrt{x} \text { come to the point }} \\ {(3 / 2,0) ?(\text {Hint} : \text { If you minimize the square of the distance, }} \\ {\text { you can avoid square roots.) }} \\ {\text { b. Graph the distance function } D(x) \text { and } y=\sqrt{x} \text { together and }} \\ {\text { reconcile what you see with your answer in part (a). }}\end{array} \end{equation}
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Applied Optimization
a. How close does the curve $y=\sqrt{x \text { come to the point }(3 / 2,0) ?}$ (Hint: If you minimize the square of the distance, you can avoid square roots.) b. Graph the distance function $D(x)$ and $y=\sqrt{x}$ together and reconcile what you see with your answer in part (a).
a. How close does the curve $y=\sqrt{x}$ come to the point $(3 / 2,0) ?$ (Hint: If you minimize the square of the distance, you can avoid square roots.) b. Graph the distance function and $y=\sqrt{x}$ together and reconcile what you see with your answer in part (a).
William S.
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