terval $a \leq t \leq b.$ As shown in Figure 1, since the vector $z'(t)$ is not zero at any point
                    $P$ on
                    $C,$ the vector
                    $z'(t)$ is tangent to $C$ at $P.$ Thus, a smooth curve has a continuously turning tangent; or in
                    other
                    words, a smooth curve can have no sharp corners or cusps. See Figure 2 for a counterexample.
                </p>

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