While doing some self-study today, I was reading through some proofs that the derivative of a Univalent Function vanishes nowhere. However, I couldn't find mention of the second derivative of a univalent function.
I thus presumed that there must be trivial counterexamples for second derivatives never vanishing; however, after testing a few simple, univalent maps I've failed to find a counterexample.
My question is thus as follows:
Can second derivatives of Univalent functions vanish somewhere?
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