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    $\begingroup$ This is helpful for solving the brachistochrone problem, but not for giving pre-solution intuition that a minimizer exists in the first place - which is what I'm asking about here. $\endgroup$ Commented 8 hours ago
  • $\begingroup$ @NoahSchweber I added to the answer. Dscussion: "What it takes to have solid expectation that a single extremum exists" $\endgroup$ Commented 6 hours ago