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We extend results of Bongiovanni et al. on double bubbles on the line withlog-convex density to the case where the derivative of the log of the densityis bounded. We show that the tie function between the double interval and thetriple interval still exists but may blow up to infinity in finite time. Forthe first time, a density is presented for which the blowup time is positiveand finite.

Double Bubbles on the Line with Log-convex Density $f$ with $(\log f)'$ Bounded