A rather normal question

Calculus Level 4

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

With point \(O\) being the origin, form the triangle \(OPQ\). Over all such triangles, what is the minimum value of the ratio of the base length \(OQ\) to the height of \(\Delta OPQ\)?

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