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- 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.
- Unless — wait: are $ d(1)=1^3 $, ..., $ d(4)=4^3 $? Yes. And $ t^3 $ interpolates exactly. So $ d(t) = t^3 $.
- The only way out is to accept $ d(t) = t^3 $, and interpret minimum depth as a misstatement, or assume the polynomial is intended to be $ t^3 $, and proceed.
- But then the statement about minimum is incompatible.
