如何畫函數(shù)y=√x(68x-103.x)的圖像示意圖

函數(shù)y=eq\r(x)(68x-eq\f(103,x))的圖像示意圖及主要性質(zhì)主要內(nèi)容：本文主要介紹根式分式復(fù)合函數(shù)y=eq\r(x)(68x-eq\f(103,x))的定義域、值域、單調(diào)和凸凹性等性質(zhì)，通過導(dǎo)數(shù)知識(shí)計(jì)算函數(shù)的單調(diào)區(qū)間和凸凹區(qū)間，畫出y=eq\r(x)(68x-eq\f(103,x))的圖像示意圖?！?函數(shù)的定義域∵eq\r(x)有x≥0；對(duì)eq\f(103,x)有x≠0.∴函數(shù)的定義域?yàn)椋?0，+∞）?！?函數(shù)的單調(diào)性∵y=eq\r(x)(68x-eq\f(103,x))=68xeq\s\up15(\f(3,2))-103xeq\s\up15(-\f(1,2)),對(duì)x求導(dǎo)得：∴eq\f(dy,dx)=eq\f(3,2)*68x*eq\s\up15(\f(1,2))+eq\f(103,2)xeq\s\up15(-\f(3,2))＞0，則：函數(shù)在定義域上為增函數(shù)?！?函數(shù)的極限lim(x→0)eq\r(x)(68x-eq\f(103,x))=-∞lim(x→+∞)eq\r(x)(68x-eq\f(103,x))=+∞?！?函數(shù)的凸凹性∵eq\f(dy,dx)=eq\f(1,2)xeq\s\up15(-\f(3,2))*(3*68x2+103)，∴eq\f(d2y,dx2)=-eq\f(3,4)*xeq\s\up15(-\f(5,2))(3*68x2+103)+3*68x*xeq\s\up15(-\f(3,2)),=-eq\f(3,4)*xeq\s\up15(-\f(5,2))(3*68x2+103)+3*68xeq\s\up15(-\f(1,2)),=-eq\f(3,4)xeq\s\up15(-\f(5,2))(3*68x2+103-4*68x2),=eq\f(3,4)xeq\s\up15(-\f(5,2))(68x2-103)>0,令eq\f(d2y,dx2)=0，則x2=eq\f(103,68).又因?yàn)閤>0，則x=eq\f(1,34)eq\r(1751)≈1.23.(1)當(dāng)x∈(0,eq\f(1,34)eq\r(1751))時(shí)，eq\f(d2y,dx2)＜0,函數(shù)y為單調(diào)凸函數(shù)；(2)當(dāng)x∈[eq\f(1,34)eq\r(1751),+∞)時(shí)，eq\f(d2y,dx2)＞0,函數(shù)y為單調(diào)凹函數(shù)?！?函數(shù)的五點(diǎn)圖x0.140.691.231.772.31eq\r(x)0.370.831.111.331.5268x-eq\f(103,x)-726.19-102.36-0.1062.17112.49y-268.69-84.96-0.1182.69170.98※.函數(shù)的圖像y=eq\r(x)(68x-eq\f(103,x))y(2.31,170.98)(1.77,82.69)(1.23