Practice question · True or false
Young's theorem guarantees for every function of two variables.
Hints
- What condition does the theorem attach?
- Continuity of the mixed partials.
Show the answer
False
Why
False. Equality holds when the mixed partials are continuous at the point. Counterexamples exist, the standard one built from has , so the hypothesis is doing real work, even though it holds for essentially every function met in economics.
Practise Partial Derivatives
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