函數(shù)y=x(99x-20.x)的圖像示意圖及主要性質(zhì)

函數(shù)y=eq\r(x)(99x-eq\f(20,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)(99x-eq\f(20,x))的定義域、值域、單調(diào)和凸凹性等性質(zhì)，通過導(dǎo)數(shù)知識計算函數(shù)的單調(diào)區(qū)間和凸凹區(qū)間，畫出y=eq\r(x)(99x-eq\f(20,x))的圖像示意圖?！?函數(shù)的定義域∵eq\r(x)有x≥0；對eq\f(20,x)有x≠0.∴函數(shù)的定義域為：(0，+∞）?！?函數(shù)的單調(diào)性∵y=eq\r(x)(99x-eq\f(20,x))=99xeq\s\up15(\f(3,2))-20xeq\s\up15(-\f(1,2)),對x求導(dǎo)得：∴eq\f(dy,dx)=eq\f(3,2)*99x*eq\s\up15(\f(1,2))+eq\f(20,2)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)(99x-eq\f(20,x))=-∞lim(x→+∞)eq\r(x)(99x-eq\f(20,x))=+∞。※.函數(shù)的凸凹性∵eq\f(dy,dx)=eq\f(1,2)xeq\s\up15(-\f(3,2))*(3*99x2+20)，∴eq\f(d2y,dx2)=-eq\f(3,4)*xeq\s\up15(-\f(5,2))(3*99x2+20)+3*99x*xeq\s\up15(-\f(3,2)),=-eq\f(3,4)*xeq\s\up15(-\f(5,2))(3*99x2+20)+3*99xeq\s\up15(-\f(1,2)),=-eq\f(3,4)xeq\s\up15(-\f(5,2))(3*99x2+20-4*99x2),=eq\f(3,4)xeq\s\up15(-\f(5,2))(99x2-20)>0,令eq\f(d2y,dx2)=0，則x2=eq\f(20,99).又因為x>0，則x=eq\f(2,33)eq\r(55)≈0.45.(1)當(dāng)x∈(0,eq\f(2,33)eq\r(55))時，eq\f(d2y,dx2)＜0,函數(shù)y為單調(diào)凸函數(shù)；(2)當(dāng)x∈[eq\f(2,33)eq\r(55),+∞)時，eq\f(d2y,dx2)＞0,函數(shù)y為單調(diào)凹函數(shù)?！?函數(shù)的五點圖x0.050.250.450.650.85eq\r(x)0.220.500.670.810.9299x-eq\f(20,x)-395.05-55.250.1133.5860.62y-86.91-27.630.0727.2055.77※.函數(shù)的圖像y=eq\r(x)(99x-eq\f(20,x))y(0.85,55.77)(0.65,27.20)(0.45