Minimum Distance from (0,0) to

Find a point on the graph of  that is closest to the origin.

We want to minimize the distance CB as C moves along the curve.

The function to minimize is the distance function for segment CB.

Use the AM-GM inequality to determine the length and the value of x for which the minimum occurs.


Make a graph showing the distance function being minimized, the minimum, and the value of x at which the minimum occurs.


Set up of the AM-GM Analysis.    Open only after you have constructed your own.