[alogo] Enclosing rectangle of rotated rectangle

Graph of the function y = f(t), t being the rotation angle of a rectangle about its gravity center and y being the area of the enclosing frame E1...E4. y obtains its maximum value when the enclosing is a square. The minimum of y occurs at multiples of π/2. How to explain that at the maximums we have tangents whereas at minimums we have only left/right tangents?

[0_0] [0_1] [0_2]
[1_0] [1_1] [1_2]

C controls the rotation angle. Switch to the "Select on contour" tool (press CTRL+2), catch and move C, to see the variation of the area (point X on the graph of function f(t)).

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