Prove: If f is a polynomial on C, then the zeros of f' are contained in the closed convex hull of the zeros of f. (Here the closed convex hull of a set S is the intersection of all closed convex sets that contain S.) [Hint: If the zeros of f are contained in a half plane V, then so are the zeros of f'.]

The Intermediate Value Theorem guarantees the existence of at least one real zero of the polynomial function f(x)= -x³ + 5x+ 5 on the following interval: 3 1 O [1,3] O [1,2] ar F1 O [-1,1] O [3, 6] F2 2 F3 #M 3 F4 LA 4 F5 % 5 F6 O Search A 6 F7 다 V F8 & 7 er + F9 * 8 €1 E a F10 28 O F11 O ) 0 F12 P Prt Sc { + 11 [ Insert } Del Backspace ] 1 11:49 PM 4/17/2023 * 7 t Home

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