Cho hàm số \(y = f(x)\) có đạo hàm trên R . Đường cong trong hình vẽ bên là đồ thị hàm số \(y = f'(x)\) , ( \(y = f'(x)\) liên tục trên R ). Xét hàm số
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Lời giải:
Báo saiTừ đồ thị thấy \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmOzayaafa % WaaeWaaeaacaWG4baacaGLOaGaayzkaaGaeyypa0JaaGimaiabgsDi % BpaadeaaeaqabeaacaWG4bGaeyypa0JaeyOeI0IaaGymaaqaaiaadI % hacqGH9aqpcaaIYaaaaiaawUfaaaaa!44F9! f'\left( x \right) = 0 \Leftrightarrow \left[ \begin{array}{l} x = - 1\\ x = 2 \end{array} \right.\) và \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmOzayaafa % WaaeWaaeaacaWG4baacaGLOaGaayzkaaGaeyOpa4JaaGimaiabgsDi % BlaadIhacqGH+aGpcaaIYaaaaa!4050! f'\left( x \right) > 0 \Leftrightarrow x > 2\)
Xét \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4zamaabm % aabaGaamiEaaGaayjkaiaawMcaaiabg2da9iaadAgadaqadaqaaiaa % dIhadaahaaWcbeqaaiaaikdaaaGccqGHsislcaaIYaaacaGLOaGaay % zkaaaaaa!4079! g\left( x \right) = f\left( {{x^2} - 2} \right)\) có TXĐ : D = R
\(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabm4zayaafa % WaaeWaaeaacaWG4baacaGLOaGaayzkaaGaeyypa0JaaGOmaiaadIha % ceWGMbGbauaadaqadaqaaiaadshaaiaawIcacaGLPaaaaaa!3FAA! g'\left( x \right) = 2xf'\left( t \right)\) với \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiDaiabg2 % da9iaadIhadaahaaWcbeqaaiaaikdaaaGccqGHsislcaaIYaaaaa!3B8C! t = {x^2} - 2\)
\(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabm4zayaafa % WaaeWaaeaacaWG4baacaGLOaGaayzkaaGaeyypa0JaaGimaiabgsDi % BpaadeaaeaqabeaacaWG4bGaeyypa0JaaGimaaqaaiaadshacqGH9a % qpcaWG4bWaaWbaaSqabeaacaaIYaaaaOGaeyOeI0IaaGOmaiabg2da % 9iabgkHiTiaaigdaaeaacaWG0bGaeyypa0JaamiEamaaCaaaleqaba % GaaGOmaaaakiabgkHiTiaaikdacqGH9aqpcaaIYaaaaiaawUfaaiab % gsDiBpaadeaaeaqabeaacaWG4bGaeyypa0JaaGimaaqaaiaadIhacq % GH9aqpcqGHXcqScaaIXaaabaGaamiEaiabg2da9iabgglaXkaaikda % aaGaay5waaaaaa!6063! g'\left( x \right) = 0 \Leftrightarrow \left[ \begin{array}{l} x = 0\\ t = {x^2} - 2 = - 1\\ t = {x^2} - 2 = 2 \end{array} \right. \Leftrightarrow \left[ \begin{array}{l} x = 0\\ x = \pm 1\\ x = \pm 2 \end{array} \right.\)
Có \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmOzayaafa % WaaeWaaeaacaWG0baacaGLOaGaayzkaaGaeyOpa4JaaGimaiabgsDi % BlaadshacqGH9aqpcaWG4bWaaWbaaSqabeaacaaIYaaaaOGaeyOeI0 % IaaGOmaiabg6da+iaaikdacqGHuhY2caWG4bGaeyipaWJaeyOeI0Ia % aGOmaiaaykW7caaMc8UaeyikIOTaaGPaVlaaykW7caWG4bGaeyOpa4 % JaaGOmaaaa!558A! f'\left( t \right) > 0 \Leftrightarrow t = {x^2} - 2 > 2 \Leftrightarrow x < - 2\,\, \vee \,\,x > 2\)
Đề thi thử tốt nghiệp THPT QG môn Toán năm 2020
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