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A2

Part of 1988 Putnam

Problems(1)

Putnam 1988 A2

Source:

8/6/2019
A not uncommon calculus mistake is to believe that the product rule for derivatives says that (fg)′=f′g′(fg)' = f'g'. If f(x)=ex2f(x)=e^{x^2}, determine, with proof, whether there exists an open interval (a,b)(a,b) and a nonzero function gg defined on (a,b)(a,b) such that this wrong product rule is true for xx in (a,b)(a,b).
Putnam