A rather normal question

Calculus Level 4

Let PP be a point (other than the origin) on the curve y=x4y = x^{4}. Let QQ be the point where the normal line to the given curve at PP intersects the xx-axis.

With point OO being the origin, form the triangle OPQOPQ. Over all such triangles, what is the minimum value of the ratio of the base length OQOQ to the height of ΔOPQ\Delta OPQ?

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