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Maximizing the area of an isosceles triangle inside a parabolic arc

An isosceles triangle has its vertex at the origin and its base parallel to the -axis with the vertices above the axis on the curve . Drag point P along this parabola. Find the coordinate of that maximize the area of the isosceles triangle. What is the maximum area this triangle can have?
Developed for use with Thomas' Calculus, published by Pearson.