Description of $C^0$ curve

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Suppose there is a curve that is already parametrized.

It is called $C^0$ continuity because there is a kink.

There are three places. which are $C^0$ $C^1$ $C^0$ respectively.

Here are the questions.

  1. Can we say "it is $C^2$ if we didn't consider those three place"?

  2. We have terminology "kink" to say $C^0$ place. What is the terminology to say $C^1$ place?