2015-12-1: Difference between revisions

Revision as of 13:42, 2 September 2023

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Problema:} Fie Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f:[-1,1]\to \mathbb{R}} o funcție crescătoare, derivabilă pe Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle [-1,1]} cu Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f'(0) \neq 0} . Să se arate ca exista cel puțin un punct Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle c \in (-1,1), c \neq 0} , cu proprietatea că $2cf(c)+\int _{0}^{c}f(x)\,dx\geq 0$ .

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Solutie (Robert Rogozsan)} Cazul Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle rom{1}}

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-Fie <math>f:[-1,1]\to \mathbb{R}</math> o funcție crescătoare, derivabilă pe <math>[-1,1]</math> cu <math>f'(0) \neq 0</math>. Să se arate ca exista cel puțin un punct <math>c \in (-1,1), c \neq 0</math>, cu proprietatea că <math>2cf(c) + \int_{0}^{c} f(x)\, dx \geq 0</math>.
+<math>Problema:</math> Fie <math>f:[-1,1]\to \mathbb{R}</math> o funcție crescătoare, derivabilă pe <math>[-1,1]</math> cu <math>f'(0) \neq 0</math>. Să se arate ca exista cel puțin un punct <math>c \in (-1,1), c \neq 0</math>, cu proprietatea că <math>2cf(c) + \int_{0}^{c} f(x)\, dx \geq 0</math>.
+<math>Solutie (Robert Rogozsan)</math>
+Cazul <math>rom{1}</math>