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Sum of Slopes at Roots

Source: 2006 Swedish Mathematical Competition #3

January 5, 2018
analytic geometrygraphing linesslopecalculusderivativealgebraSweden

Problem Statement

A cubic polynomial ff with a positive leading coefficient has three different positive zeros. Show that f′(a)+f′(b)+f′(c)>0f'(a)+ f'(b)+ f'(c) > 0.
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