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Home » The sum of the first and fifth terms is: - Redraw

The sum of the first and fifth terms is: - Redraw

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 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.

📌 Unless the values are not exact? But they are given as exact.

📌 Alternative: the problem says d depicts... as a cubic polynomial — so $ d(t) $ is cubic, and matches $ t^3 $ at $ t=1,2,3,4 $. But maybe the minimum condition is used to confirm uniqueness? But we already have uniqueness from interpolation.

📌 Wait — perhaps the minimum depth is not global, but local? But $ t^3 $ has no local minimum.

📌 Unless the domain is bounded? But no domain is specified.

📌 But the oceanographer context suggests time $ t \geq 0 $, and $ d(t) $ likely defined on $ \mathbb{R}_{\geq 0} $. Still, $ t^3 $ has no local minimum on $ [0, \infty) $.

📌 Thus, contradiction — unless $ d(t) $ is not $ t^3 $, so our earlier interpolation must be reconsidered.

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