2015-12-1: Difference between revisions
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Fie <math>f:[-1,1]\to \mathbb{R}</math> o funcție crescătoare, derivabila pe <math>[-1,1]</math> cu <math>f'(0) \neq 0</math>. Sa se arate ca exista cel putin un punct <math>c \in (-1,1), c \neq 0</math>, cu proprietatea ca <math>2cf(c) + \int_{0}{c} f(x)\, dx \geq 0</math>. | Fie <math>f:[-1,1]\to \mathbb{R}</math> o funcție crescătoare, derivabila pe <math>[-1,1]</math> cu <math>f'(0) \neq 0</math>. Sa se arate ca exista cel putin un punct <math>c \in (-1,1), c \neq 0</math>, cu proprietatea ca <math>2cf(c) + \int_{0}^{c} f(x)\, dx \geq 0</math>. | ||
Revision as of 13:38, 2 September 2023
Fie o funcție crescătoare, derivabila 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} . Sa se arate ca exista cel putin 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 ca .
![{\displaystyle f:[-1,1]\to \mathbb {R} }](https://wikimedia.org/api/rest_v1/media/math/render/svg/1bd6b3e94215c6224a6e70a62a912110cbf6a249)
