This is equivalent to the following result: If all critical points of a rational function lie on a circle in the Riemann sphere (for example, on the real line), then the function maps this circle into ...

Tsai-Han Kiang, On the Existence of Critical Points of Green's Functions for Three-Dimensional Regions, American Journal of Mathematics, Vol. 54, No. 4 (Oct., 1932), pp. 657-666 ...

Determine the critical points of \ (f\text {.}\) Determine the intervals on which the function is increasing or decreasing. Classify the critical point (s) as either local maxima, local minima, or ...