Cho y = f(x) mà đồ thị hàm số y = f'(x) như hình vẽ bên

Bất phương trình \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzamaabm % aabaGaamiEaaGaayjkaiaawMcaaiabg6da+iGacohacaGGPbGaaiOB % amaalaaabaGaeqiWdaNaamiEaaqaaiaaikdaaaGaey4kaSIaamyBaa % aa!429F! f\left( x \right) > \sin \frac{{\pi x}}{2} + m\) nghiệm đúng với mọi \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEaiabgI % GiopaadmaabaGaeyOeI0IaaGymaiaacUdacaaIZaaacaGLBbGaayzx % aaaaaa!3D8B! x \in \left[ { - 1;3} \right]\) khi và chỉ khi:

A. m < f(0)

B. m < f(1) - 1

C. m < f(-1) + 1

D. m < f(2)

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Chủ đề: Đề thi THPT QG

Môn: Toán

Lời giải:

Báo sai

\(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaWGMb % WaaeWaaeaacaWG4baacaGLOaGaayzkaaGaeyOpa4Jaci4CaiaacMga % caGGUbWaaSaaaeaacqaHapaCcaWG4baabaGaaGOmaaaacqGHRaWkca % WGTbGaeyiaIiIaamiEaiabgIGiopaadmaabaGaeyOeI0IaaGymaiaa % cUdacaaIZaaacaGLBbGaayzxaaGaeyi1HSTaam4zamaabmaabaGaam % iEaaGaayjkaiaawMcaaiabg2da9iaadAgadaqadaqaaiaadIhaaiaa % wIcacaGLPaaacqGHsislciGGZbGaaiyAaiaac6gadaWcaaqaaiabec % 8aWjaadIhaaeaacaaIYaaaaiabg6da+iaad2gacqGHaiIicaWG4bGa % eyicI48aamWaaeaacqGHsislcaaIXaGaai4oaiaaiodaaiaawUfaca % GLDbaaaeaacqGHshI3caWGTbGaeyipaWZaaCbeaeaaciGGTbGaaiyA % aiaac6gaaSqaamaadmaabaGaeyOeI0IaaGymaiaacUdacaaIZaaaca % GLBbGaayzxaaaabeaakiaadEgadaqadaqaaiaadIhaaiaawIcacaGL % Paaaaaaa!76EE! \begin{array}{l} f\left( x \right) > \sin \frac{{\pi x}}{2} + m\forall x \in \left[ { - 1;3} \right] \Leftrightarrow g\left( x \right) = f\left( x \right) - \sin \frac{{\pi x}}{2} > m\forall x \in \left[ { - 1;3} \right]\\ \Rightarrow m < \mathop {\min }\limits_{\left[ { - 1;3} \right]} g\left( x \right) \end{array}\)

Từ đồ thị hàm số y = f'(x) ta suy ra BBT đồ thị hàm số y = f(x) như sau:

Dựa vào BBT ta thấy \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzamaabm % aabaGaamiEaaGaayjkaiaawMcaaiabgwMiZkaadAgadaqadaqaaiaa % igdaaiaawIcacaGLPaaacqGHaiIicaWG4bGaeyicI48aamWaaeaacq % GHsislcaaIXaGaai4oaiaaiodaaiaawUfacaGLDbaaaaa!46C1! f\left( x \right) \ge f\left( 1 \right)\forall x \in \left[ { - 1;3} \right]\)

\(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaWG4b % GaeyicI48aamWaaeaacqGHsislcaaIXaGaai4oaiaaiodaaiaawUfa % caGLDbaacqGHshI3daWcaaqaaiabec8aWjaadIhaaeaacaaIYaaaai % abgIGiopaadmaabaGaeyOeI0YaaSaaaeaacqaHapaCaeaacaaIYaaa % aiaacUdadaWcaaqaaiaaiodacqaHapaCaeaacaaIYaaaaaGaay5wai % aaw2faaiabgkDiElabgkHiTiaaigdacqGHKjYOciGGZbGaaiyAaiaa % c6gadaWcaaqaaiabec8aWjaadIhaaeaacaaIYaaaaiabgsMiJkaaig % daaeaacqGHuhY2cqGHsislcaaIXaGaeyizImQaeyOeI0Iaci4Caiaa % cMgacaGGUbWaaSaaaeaacqaHapaCcaWG4baabaGaaGOmaaaacqGHKj % YOcaaIXaaabaGaeyO0H4TaamOzamaabmaabaGaaGymaaGaayjkaiaa % wMcaaiabgkHiTiaaigdacqGHKjYOcaWGMbWaaeWaaeaacaWG4baaca % GLOaGaayzkaaGaeyOeI0Iaci4CaiaacMgacaGGUbWaaSaaaeaacqaH % apaCcaWG4baabaGaaGOmaaaacqGHuhY2caWGNbWaaeWaaeaacaWG4b % aacaGLOaGaayzkaaGaeyyzImRaamOzamaabmaabaGaaGymaaGaayjk % aiaawMcaaiabgkHiTiaaigdacqGHshI3daWfqaqaaiGac2gacaGGPb % GaaiOBaaWcbaWaamWaaeaacqGHsislcaaIXaGaai4oaiaaiodaaiaa % wUfacaGLDbaaaeqaaOGaam4zamaabmaabaGaamiEaaGaayjkaiaawM % caaiabg2da9iaadAgadaqadaqaaiaaigdaaiaawIcacaGLPaaacqGH % sislcaaIXaaaaaa!A04A! \begin{array}{l} x \in \left[ { - 1;3} \right] \Rightarrow \frac{{\pi x}}{2} \in \left[ { - \frac{\pi }{2};\frac{{3\pi }}{2}} \right] \Rightarrow - 1 \le \sin \frac{{\pi x}}{2} \le 1\\ \Leftrightarrow - 1 \le - \sin \frac{{\pi x}}{2} \le 1\\ \Rightarrow f\left( 1 \right) - 1 \le f\left( x \right) - \sin \frac{{\pi x}}{2} \Leftrightarrow g\left( x \right) \ge f\left( 1 \right) - 1 \Rightarrow \mathop {\min }\limits_{\left[ { - 1;3} \right]} g\left( x \right) = f\left( 1 \right) - 1 \end{array}\)

Vậy \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyBaiabgY % da8iaadAgadaqadaqaaiaaigdaaiaawIcacaGLPaaacqGHsislcaaI % Xaaaaa!3CC1! m < f\left( 1 \right) - 1\)

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