In Churchill’s complex variables book he defined a smooth contour z(t) as a parameterized curve over some continuous closed interval a <= t <= b where z'(t) is nonzero throughout the open interval a < t < b.
What would a point p such that z'(p) = 0 look like along a curve? I assumed that such a point would like a local extrema from calculus but the existance of closed contours contradicts this.
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