Find the point P on the graph of the function y=√x closest to the point (9,0) The x coordinate of P is:

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Step-by-step explanation:

Let the -coordinate of be . For to be on the graph of the function , the -coordinate of would need to be . Therefore, the coordinate of would be .

The Euclidean Distance between and is:

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The goal is to find the a that minimizes this distance. However, is non-negative for all real . Hence, the that minimizes the square of this expression, , would also minimize .

Differentiate with respect to :

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Set the first derivative, , to and solve for :

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Notice that the second derivative is greater than for this . Hence, would indeed minimize . This value would also minimize , the distance between and .

Therefore, the point would be closest to when the -coordinate of is .