• 2022-07-25
    求下面函数的单调增减区间:[tex=5.857x1.357]vcG802Y4Fd8qOKpq/5MEvQsekRQaMwxWvyx7epdELco=[/tex]
  • 解:[tex=5.857x1.357]vcG802Y4Fd8qOKpq/5MEvQsekRQaMwxWvyx7epdELco=[/tex] 的定义域为 [tex=4.929x1.357]WafKDm5071vVz9IYJgBhj0yJnnoyrKF945lfWaql7dc=[/tex] 若 [tex=4.643x1.214]ZBDl8uI0kMoamHo/L1HPvT9aZLMq3VsqlLW0KCCZhsA=[/tex] 于是 [tex=17.071x1.429]W3aOnEkEB93blPtW72U+Cr3cmFeADBeVDW+Jo1HVgfIRYylrbue83aoMOc/gTkIe0fSe+iC01jVSpjbVI+/DOw==[/tex] 得 [tex=3.0x2.357]W/mzqB/NbayHlhA5Vs6rCDbAN8JzYsjsjJ/nhQZbBS0=[/tex]。当 [tex=5.214x2.357]t7ovh1xwi5H46X25E42qLIa/T6YQ04VPWzyMKpcy7bfbvPBR0D5jUDnNmHSxk0UF[/tex] 时, [tex=2.357x1.357]RTkfYK9HWUq35/9CP+KfMs59hl2fOtqitPQVzJ+6zFo=[/tex] 当 [tex=8.429x2.357]Bg7UtpPt6gCyVQ2vIJT65/7OZhj3BoSyA6Hk4X7K1QcM45wk2boQBG85nooIRI20AYw+sJcoDNPC4IyPG0SmJw==[/tex] 注意到 [tex=0.5x1.0]yBR4oiFoTexGaFalQ7m8kg==[/tex] 的周期性,当 [tex=8.571x2.357]ck/SOOTum4h9SS4SfgD1tKqoJ56+s/TUaFKM0mI0R3jDRNSY+qzeBhMpWnezqqcoLXuaPJ3Pza1bAeagDMNxzQ==[/tex] 即 [tex=7.286x2.357]fZG67YvQvNeldoTO6gvGqeNNcxl+6DBapWnS5kZ2xZ9EoCBXNWqk2Ff4zMRNFwGy[/tex]  时, [tex=10.786x1.429]d2lhz1/u1LozWn20xdJgSPRmhwBjTKPj9EvdwicvVeq/9L5sH4BVJSLbonxy+jsA[/tex] 函数单调增。当 [tex=10.429x2.357]NLU/MBWWw5vT94XEh++bqvxa2xzOa0jV2GEn20iCoGErM709IDqkdtog7tq9jc7tT3XezisE5H6IX7i1QxzfUA==[/tex] 即 [tex=9.071x2.357]XrbVqnco8Q7O+CtN8Vu/RrrvJYhJM4zsj3O3FBIXcWfN+tHJUJQIgndnk9uAfcOK+746X6RfbIa4h5bGM6+Qbw==[/tex] 时 [tex=8.786x1.357]YhKGfJD3Pmh7EBa6eX9ZH26QWhcO1I/l6YACF9ojH18=[/tex] 函数单调减。若 [tex=4.643x1.214]sA1HS10F7q8yLP7XyQpi0g==[/tex] 于是 [tex=10.286x1.357]nqXEdtFO0hCXLHDXAh6eb0C08M/G+FZAMt7zGKxRtXH1qRXztkppXDXwhA3pqZTe[/tex] 由 [tex=7.643x1.357]BIZpdf9VkP1tnmfpXslrvkdf9bURET+3efkLbEa74D8=[/tex] 可得 [tex=3.786x2.357]gWoZ47xBoMeODpVFGKTYVKzYeYKzB5pDRlHYel0rv6U=[/tex] 当 [tex=5.286x2.357]cRNdlEH9wAKDM+bSCpyAuRdSVrCwOgWoK3WkA+IMK432XUqdwB/AFYG+cY4ty13t[/tex] 时, [tex=2.357x1.357]RTkfYK9HWUq35/9CP+KfMs59hl2fOtqitPQVzJ+6zFo=[/tex] 当 [tex=5.786x2.357]8klhIKOMJ7uRX1SsIm4lpCxrSJkvqGKf5ryn14D+iqJ4Z07HpMPLyxNNJ5q/zyUd[/tex] 时, [tex=2.929x1.357]f8Il6MoVSeUfqo9pSAKLdYFO2725JbFMw4O+YPnIOVk=[/tex] 于是当 [tex=17.714x2.357]9CgZfuYpLMkbvzsjQpMbsklW+ix+r4RHyOlmUP4TjdB1DS6qzWIWLWPZdzR/NUkn2GejWHBZfPMM4WZFATE9VKGLumra14pa003Cn9ZTlhF2jZMEcGxwoa2MwLJF16sg[/tex] 时, [tex=2.071x1.357]Lm96azQDEL3KOz8qAwJjXg==[/tex],函数单调增;当 [tex=14.714x1.357]9IHjUSnM3j6qgXiopy90FhzMN9qTJUfRAwWluR65cIz08AI7Q4jYWIg8duR0zfVzHhl24CICuAwWg6v7VxqBIw==[/tex] 时, [tex=2.929x1.357]GzusXhtaMOhRGtOTgmzN6g==[/tex] 函数单调jian

    内容

    • 0

      求函数 [tex=5.143x1.571]OCj21ozeJQpB0WoBh2AdZF6fxdI5bV3paTQyBfJIzzU=[/tex]的单调区间

    • 1

      求函数 [tex=5.786x1.643]wyIZoKZPebPDMsT9Vyfv3asTwexMZCnezcS7LDEujK4=[/tex]的单调区间

    • 2

      求函数[tex=6.214x1.286]7rd2QsTj5+9CXTGrU7h3v2Ucx3rapU3sXsiKZWfWM00=[/tex]的单调区间。

    • 3

      求函数[tex=9.214x1.786]yrrO3SEcIf8tb28X5T3qnPXG7Vvjig9bedOl8ENBXO8DjbvqN4pixPnCod+7Nwje[/tex]的单调区间。

    • 4

      求函数[tex=5.786x1.429]XxC1uCUli2Guku72pW7HjYV6YrhFImb96mRPkeyPL70=[/tex]的单调区间。