函數(shù)y=√x(79x-5.x)的圖像示意圖及其性質(zhì)

函數(shù)y=eq\r(x)(79x-eq\f(5,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)(79x-eq\f(5,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)(79x-eq\f(5,x))的圖像示意圖?！?函數(shù)的定義域∵eq\r(x)有x≥0；對eq\f(5,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)(79x-eq\f(5,x))=79xeq\s\up15(\f(3,2))-5xeq\s\up15(-\f(1,2)),對x求導(dǎo)得：∴eq\f(dy,dx)=eq\f(3,2)*79x*eq\s\up15(\f(1,2))+eq\f(5,2)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)(79x-eq\f(5,x))=-∞lim(x→+∞)eq\r(x)(79x-eq\f(5,x))=+∞。※.函數(shù)的凸凹性∵eq\f(dy,dx)=eq\f(1,2)xeq\s\up15(-\f(3,2))*(3*79x2+5)，∴eq\f(d2y,dx2)=-eq\f(3,4)*xeq\s\up15(-\f(5,2))(3*79x2+5)+3*79x*xeq\s\up15(-\f(3,2)),=-eq\f(3,4)*xeq\s\up15(-\f(5,2))(3*79x2+5)+3*79xeq\s\up15(-\f(1,2)),=-eq\f(3,4)xeq\s\up15(-\f(5,2))(3*79x2+5-4*79x2),=eq\f(3,4)xeq\s\up15(-\f(5,2))(79x2-5)>0,令eq\f(d2y,dx2)=0，則x2=eq\f(5,79).又因為x>0，則x=eq\f(1,79)eq\r(395)≈0.25.(1)當(dāng)x∈(0,eq\f(1,79)eq\r(395))時，eq\f(d2y,dx2)＜0,函數(shù)y為單調(diào)凸函數(shù)；(2)當(dāng)x∈[eq\f(1,79)eq\r(395),+∞)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x0.030.140.250.360.47eq\r(x)0.170.370.500.600.6979x-eq\f(5,x)-164.30-24.65-0.2514.5526.49y-27.93-9.12-0.138.7318.28※.函數(shù)的圖像y=eq\r(x)(79x-eq\f(5,x))y(0.47,18.28)(0.36,8.73)(0.25,