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Mathematical Argument and Justification
Grade Level
Calculus I
CAL1.178 Mathematical Argument and Justification
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A model for error e(x) is continuous on [0,10). A student claims: “By the Extreme Value Theorem, e has an absolute minimum on [0,10).” Which critique is strongest?
A
The claim is correct because [0,10) is bounded, so it is effectively closed.
B
The interval is not closed because it does not include 10; EVT requires a closed interval. The function could approach its infimum as x approaches 10 without attaining it.
C
The claim is false because continuous functions never have minima.
D
The claim is correct only if e(0)=0.
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