Problem #PRU-107768

Problems Calculus Real numbers Integer and fractional parts. Archimedean property Methods Pigeonhole principle Pigeonhole principle (other)

Problem

A cherry which is a ball of radius r is dropped into a round glass whose axial section is the graph of the function \(y = x^4\). At what maximum r will the ball touch the most bottom point of the bottom of the glass? (In other words, what is the maximum radius r of a circle lying in the region \(y \geq x^4\) and containing the origin?).