{"id":705,"date":"2024-04-20T10:47:35","date_gmt":"2024-04-20T10:47:35","guid":{"rendered":"https:\/\/gbelentzas.sites.sch.gr\/?p=705"},"modified":"2024-05-01T07:44:38","modified_gmt":"2024-05-01T07:44:38","slug":"%ce%b8%ce%b5%cf%8e%cf%81%ce%b7%ce%bc%ce%b1-fermat-%ce%b1%cf%80%cf%8c%ce%b4%ce%b5%ce%b9%ce%be%ce%b7","status":"publish","type":"post","link":"https:\/\/gbelentzas.sites.sch.gr\/?p=705","title":{"rendered":"\u0398\u03b5\u03ce\u03c1\u03b7\u03bc\u03b1 Fermat (\u03b1\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7)"},"content":{"rendered":"

\u0398\u03b5\u03ce\u03c1\u03b7\u03bc\u03b1 18. <\/strong>(\u0398. Fermat) \u0388\u03c3\u03c4\u03c9 \u03bc\u03b9\u03b1 \u03c3\u03c5\u03bd\u03ac\u03c1\u03c4\u03b7\u03c3\u03b7<\/span> \"\textcolor{blue}{ f}\" \u03bf\u03c1\u03b9\u03c3\u03bc\u03ad\u03bd\u03b7 \u03c3’ \u03ad\u03bd\u03b1 \u03b4\u03b9\u03ac\u03c3\u03c4\u03b7\u03bc\u03b1 \u0394 \u03ba\u03b1\u03b9<\/span> \"\textcolor{blue}{ x_0}\" \u03ad\u03bd\u03b1 \u03b5\u03c3\u03c9\u03c4\u03b5\u03c1\u03b9\u03ba\u03cc \u03c3\u03b7\u03bc\u03b5\u03af\u03bf \u03c4\u03bf\u03c5 \u0394. \u0391\u03bd \u03b7<\/span> \"\textcolor{blue}{ f}\" \u03c0\u03b1\u03c1\u03bf\u03c5\u03c3\u03b9\u03ac\u03b6\u03b5\u03b9 \u03c4\u03bf\u03c0\u03b9\u03ba\u03cc \u03b1\u03ba\u03c1\u03cc\u03c4\u03b1\u03c4\u03bf \u03c3\u03c4\u03bf<\/span> \"\textcolor{blue}{x_0}\" \u03ba\u03b1\u03b9 \u03b5\u03af\u03bd\u03b1\u03b9 \u03c0\u03b1\u03c1\u03b1\u03b3\u03c9\u03b3\u03af\u03c3\u03b9\u03bc\u03b7 \u03c3\u03c4\u03bf \u03c3\u03b7\u03bc\u03b5\u03af\u03bf \u03b1\u03c5\u03c4\u03cc, \u03c4\u03cc\u03c4\u03b5 \u03bd\u03b1 \u03b1\u03c0\u03bf\u03b4\u03b5\u03af\u03be\u03b5\u03c4\u03b5 \u03cc\u03c4\u03b9:<\/span><\/p>\n

  <\/span>   <\/span>\"\[\textcolor{blue}{ f '(x_0) = 0}\]\"<\/p>\n

(\u0397\u039c. 2004, \u0397\u039c. 2011)<\/span><\/em><\/p>\n

\n

\u0388\u03c3\u03c4\u03c9 \u03bc\u03b9\u03b1 \u03c3\u03c5\u03bd\u03ac\u03c1\u03c4\u03b7\u03c3\u03b7 \"f\" \u03bf\u03c1\u03b9\u03c3\u03bc\u03ad\u03bd\u03b7 \u03c3’ \u03ad\u03bd\u03b1 \u03b4\u03b9\u03ac\u03c3\u03c4\u03b7\u03bc\u03b1 \u0394 \u03ba\u03b1\u03b9 \"x_0\" \u03ad\u03bd\u03b1 \u03b5\u03c3\u03c9\u03c4\u03b5\u03c1\u03b9\u03ba\u03cc \u03c3\u03b7\u03bc\u03b5\u03af\u03bf \u03c4\u03bf\u03c5 \u0394.<\/p>\n

\u0391\u03c2 \u03c5\u03c0\u03bf\u03b8\u03ad\u03c3\u03bf\u03c5\u03bc\u03b5 \u03cc\u03c4\u03b9 \u03b7 f \u03c0\u03b1\u03c1\u03bf\u03c5\u03c3\u03b9\u03ac\u03b6\u03b5\u03b9 \u03c3\u03c4\u03bf \"x_0\" \u03c4\u03bf\u03c0\u03b9\u03ba\u03cc \u03bc\u03ad\u03b3\u03b9\u03c3\u03c4\u03bf.<\/p>\n

\u0395\u03c0\u03b5\u03b9\u03b4\u03ae \u03c4\u03bf \"x_0\" \u03b5\u03af\u03bd\u03b1\u03b9 \u03b5\u03c3\u03c9\u03c4\u03b5\u03c1\u03b9\u03ba\u03cc \u03c3\u03b7\u03bc\u03b5\u03af\u03bf \u03c4\u03bf\u03c5 \u0394 \u03ba\u03b1\u03b9 \u03b7 \"f\" \u03c0\u03b1\u03c1\u03bf\u03c5\u03c3\u03b9\u03ac\u03b6\u03b5\u03b9 \u03c3’ \u03b1\u03c5\u03c4\u03cc \u03c4\u03bf\u03c0\u03b9\u03ba\u03cc \u03bc\u03ad\u03b3\u03b9\u03c3\u03c4\u03bf, \u03c5\u03c0\u03ac\u03c1\u03c7\u03b5\u03b9 \"\delta > 0\" \u03c4\u03ad\u03c4\u03bf\u03b9\u03bf, \u03ce\u03c3\u03c4\u03b5<\/p>\n

 <\/p>\n

\"(x_0 - \delta , x_0 + \delta)\subseteq \Delta\" \u03ba\u03b1\u03b9 \"f(x) \leq f(x_0)\" \u00a0 \u03b3\u03b9\u03b1 \u03ba\u03ac\u03b8\u03b5 \"x \in (x_0 - \delta , x_0 +\delta) \quad (1)\"<\/p>\n

\u0395\u03c0\u03b5\u03b9\u03b4\u03ae, \u03b5\u03c0\u03b9\u03c0\u03bb\u03ad\u03bf\u03bd, \u03b7 \"f\" \u03b5\u03af\u03bd\u03b1\u03b9 \u03c0\u03b1\u03c1\u03b1\u03b3\u03c9\u03b3\u03af\u03c3\u03b9\u03bc\u03b7 \u03c3\u03c4\u03bf \"x_0,\" \u03b9\u03c3\u03c7\u03cd\u03b5\u03b9<\/p>\n

  <\/span>   <\/span>\"\[f^{\prime}\left(x_{0}\right)=\lim _{x \rightarrow x_{0}^{-}} \dfrac{f(x)-f\left(x_{0}\right)}{x-x_{0}}=\lim _{x \rightarrow x_{0}^{+}} \dfrac{f(x)-f\left(x_{0}\right)}{x-x_{0}}\]\"<\/p>\n

\u0395\u03c0\u03bf\u03bc\u03ad\u03bd\u03c9\u03c2,<\/p>\n