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Find the point on the graph of the function that is closest to the given point.

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To find the point on the graph of the function that is closest to the point , we first need to express the distance between a generic point on the function, , and the point . The distance can be given by the formula:

Substituting :

To minimize the distance, you can minimize instead to avoid dealing with the square root. So now you can formulate:

Now, differentiate with respect to , set the derivative equal to zero, and solve the resulting equation to find the x-coordinate of the closest point. Don’t forget to check that because the function is defined only for .

Lastly, plug this value back into the function to get the corresponding value. You’ll find a point that you can express as .

Let me know if you need further assistance!