MATH.10:8 - Common Anti-Patterns and How to Avoid Them

Observed or text-invited mistake	Repair
Vary each allocation independently while retaining a fixed-total claim.	Couple the changes so the total remains fixed and derive their allowed range.
Use a tangent displacement as a finite feasible move on a curved constraint.	Construct a feasible curve or retain only the first-order conclusion supported by the tangent argument.
Accept a zero derivative as a minimum.	Determine the remaining change or use a sufficiency theorem with its hypotheses.
Reject a boundary optimum because its unrestricted derivative is nonzero.	Test the available one-sided or constrained changes.
Apply a small-step sign to an arbitrarily large step.	Calculate the finite difference or bound the remainder over that step.
Declare global optimality after testing one restricted family.	Supply the missing coverage or limit the conclusion to that family.