Cho hàm số \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaiaacI % cacaWG4bGaaiykaiabg2da9maaceaaeaqabeaacaWG4bWaaWbaaSqa % beaacaaIYaaaaOGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGa % GaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabcca % caqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiai % aabccacaqGRbGaaeiAaiaabMgacaqGGaGaaeiiaiaabccacaWG4bGa % eyizImQaaGOmaaqaaiabgkHiTmaalaaabaGaamiEamaaCaaaleqaba % GaaGOmaaaaaOqaaiaaikdaaaGaey4kaSIaamOyaiaadIhacqGHsisl % caaI2aGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiai % aabUgacaqGObGaaeyAaiaabccacaqGGaGaaeiiaiaabccacaWG4bGa % eyOpa4JaaGOmaaaacaGL7baaaaa!68AF! f(x) = \left\{ \begin{array}{l} {x^2}{\rm{ khi }}x \le 2\\ - \frac{{{x^2}}}{2} + bx - 6{\rm{ khi }}x > 2 \end{array} \right.\). Để hàm số này có đạo hàm tại x = 2 thì giá trị của b là

Ta có

\(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacqGHIa % YTdaWgaaWcbaaabeaakiaadAgadaqadaqaaiaaikdaaiaawIcacaGL % PaaacqGH9aqpcaaI0aaabaGaeyOiGC7aaSbaaSqaaaqabaGcdaWfqa % qaaiGacYgacaGGPbGaaiyBaaWcbaGaamiEaiabgkziUkaaikdadaah % aaadbeqaaiabgkHiTaaaaSqabaGccaWGMbWaaeWaaeaacaWG4baaca % GLOaGaayzkaaGaeyypa0ZaaCbeaeaaciGGSbGaaiyAaiaac2gaaSqa % aiaadIhacqGHsgIRcaaIYaWaaWbaaWqabeaacqGHsislaaaaleqaaO % GaamiEamaaCaaaleqabaGaaGOmaaaakiabg2da9iaaisdaaeaacqGH % IaYTdaWgaaWcbaaabeaakmaaxababaGaciiBaiaacMgacaGGTbaale % aacaWG4bGaeyOKH4QaaGOmamaaCaaameqabaGaeyOeI0caaaWcbeaa % kiaadAgadaqadaqaaiaadIhaaiaawIcacaGLPaaacqGH9aqpdaWfqa % qaaiGacYgacaGGPbGaaiyBaaWcbaGaamiEaiabgkziUkaaikdadaah % aaadbeqaaiabgkHiTaaaaSqabaGcdaqadaqaaiabgkHiTmaalaaaba % GaamiEamaaCaaaleqabaGaaGOmaaaaaOqaaiaaikdaaaGaey4kaSIa % amOyaiaadIhacqGHsislcaaI2aaacaGLOaGaayzkaaGaeyypa0JaaG % OmaiaadkgacqGHsislcaaI4aaaaaa!7A3B! \begin{array}{l} { \bullet _{}}f\left( 2 \right) = 4\\ { \bullet _{}}\mathop {\lim }\limits_{x \to {2^ - }} f\left( x \right) = \mathop {\lim }\limits_{x \to {2^ - }} {x^2} = 4\\ { \bullet _{}}\mathop {\lim }\limits_{x \to {2^ - }} f\left( x \right) = \mathop {\lim }\limits_{x \to {2^ - }} \left( { - \frac{{{x^2}}}{2} + bx - 6} \right) = 2b - 8 \end{array}\)

 f(x) có đạo hàm tại x = 2  khi và chỉ khi f(x) liên tục tại x = 2

\(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyi1HS9aaC % beaeaaciGGSbGaaiyAaiaac2gaaSqaaiaadIhacqGHsgIRcaaIYaWa % aWbaaWqabeaacqGHsislaaaaleqaaOGaamOzamaabmaabaGaamiEaa % GaayjkaiaawMcaaiabg2da9maaxababaGaciiBaiaacMgacaGGTbaa % leaacaWG4bGaeyOKH4QaaGOmamaaCaaameqabaGaeyOeI0caaaWcbe % aakiaadAgadaqadaqaaiaadIhaaiaawIcacaGLPaaacqGH9aqpcaWG % MbWaaeWaaeaacaaIYaaacaGLOaGaayzkaaGaeyi1HSTaaGOmaiaadk % gacqGHsislcaaI4aGaeyypa0JaaGinaiabgsDiBlaadkgacqGH9aqp % caaI2aGaaiOlaaaa!6158! \Leftrightarrow \mathop {\lim }\limits_{x \to {2^ - }} f\left( x \right) = \mathop {\lim }\limits_{x \to {2^ - }} f\left( x \right) = f\left( 2 \right) \Leftrightarrow 2b - 8 = 4 \Leftrightarrow b = 6.\)