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📰 But $ d(t) $ agrees with $ t^3 $ at $ t=1,2,3,4 $, yet is a cubic. So define $ p(t) = d(t) - t^3 $. Then $ p(t) $ is a polynomial of degree at most 3 (since $ d(t) $ is cubic, $ t^3 $ is cubic), and $ p(1) = p(2) = p(3) = p(4) = 0 $. 📰 So $ p(t) $ has four roots and is degree ≤ 3 → $ p(t) \equiv 0 $. Hence $ d(t) = t^3 $ is the only possibility. 📰 Therefore, the requirement of a minimum must be interpreted carefully. But the problem says achieves its minimum depth exactly once — so perhaps minimum is a red herring, or we are to assume $ d(t) $ has a unique global minimum, but only one cubic satisfies the four points. 📰 Rainbow Bagels 4264604 📰 Boca Raton Boca Beach Club A Waldorf Astoria Resort 5164840 📰 Arrabiata Sauce Recipe 3353354 📰 The Ultimate Guide To Calacatta Marble Why Its The Most Coveted Stone In Design 7745207 📰 No Voice No Problem Sing Like Never Before With This Top Singing App 2359464 📰 Airport Tycoon 182469 📰 Flowers That Bloom In Late Winter 9832177 📰 Youll Be Shocked Download The Secret Face Detection Camera App Now 748989 📰 Publick House Inn And Lodge 8586927 📰 Whats An Erp System The Simple Guide That Will Change How You Run Your Business 9386803 📰 Indiana Basketbakk 5103329 📰 Aunt Bertas Kitchen 6517934 📰 Speak To Save Time The Ultimate Guide To Smarter Voice To Text Technology 6193476 📰 How Much Did Kevin Spend In Home Alone 2 73 📰 Unlock Et Stock Secrets Expert Analysis You Need To Know Before It Goes Viral 154733