# 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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