函數(shù)y=eq\f(123x3,119x2+225)的圖像畫法及性質(zhì)解析主要內(nèi)容：本文主要函數(shù)y=eq\f(123x3,119x2+225)的定義域、值域、單調(diào)性、奇偶性、凸凹性等性質(zhì)異同點(diǎn)，并簡(jiǎn)要畫出函數(shù)y=eq\f(123x3,119x2+225)的圖像示意圖。函數(shù)的定義域：∵分母119x2+225≥225＞0，即分母為正的實(shí)數(shù)，再取倒數(shù)函數(shù)有意義?！嗪瘮?shù)的定義域?yàn)槿w實(shí)數(shù)，即定義域均為：(-∞，+∞)。函數(shù)的單調(diào)性：用導(dǎo)數(shù)工具解析單調(diào)性為：∵y=eq\f(123x3,119x2+225),∴eq\f(dy,dx)=eq\f(3*123x2*(119x2+225)-2*119*123x?,(119x2+225)2)=eq\f(123x2(119x2+3*225),(119x2+225)2)＞0，可知函數(shù)y在定義域上為單調(diào)增函數(shù)。函數(shù)的凸凹性：eq\f(dy,dx)=123*eq\f(119x?+3*225x2,(119x2+225)2);eq\f(d2y,dx2)=123*eq\f((4*119x3+6*225x)(119x2+225)2-(119x?+3*225x2)*4*119x(119x2+225),(119x2+225)?)=2*123x*eq\f((2*119x2+3*225)(119x2+225)-2*119(119x?+3*225x2),(119x2+225)3)=-2*225*123x*eq\f(119x2-3*2252,(119x2+225)3).令eq\f(d2y,dx2)=0，則x=0或者119x2-3*2252=0，求出x=±eq\f(15,119)eq\r(357)≈±2.38，函數(shù)y凸凹性為：(1)當(dāng)x∈[-2.38，0]∪(2.38,+∞)時(shí)，eq\f(d2y,dx2)≤0，則函數(shù)y為凸函數(shù)；(2)當(dāng)x∈(-∞,-2.38)∪(0,2.38]時(shí)，eq\f(d2y,dx2)>0，則函數(shù)y為凹函數(shù)。函數(shù)的奇偶性：因?yàn)閒(x)=eq\f(123x3,119x2+225),所以f(-x)=eq\f(123(-x)3,119(-x)2+225)=-eq\f(123x3,119x2+225)=-f(x).所以函數(shù)f(x)為奇函數(shù)，圖像關(guān)于原點(diǎn)對(duì)稱。函數(shù)的極限：Lim(x→-∞)eq\f(123x3,119x2+225)=-∞，Lim(x→+∞)eq\f(123x3,119x2+225)=+∞，Lim(x→0+)eq\f(123x3,119x2+225)=0，Lim(x→0-)eq\f(123x3,119x2+225)=0.函數(shù)的特征點(diǎn)圖表：x-4.76-3.57-2.38-1.1901.192.383.574.76123x3-13265.57-5596.41-1658.20-207.270207.271658.205596.4113265.57119x2+2252921.251741.64899.06393.52225393.52899.061741.642921.25y-4.541-3.213-1.844-0.52700.5271.843.2134.541函數(shù)的圖像示意圖：y=eq\f(123x3,119x2+225)y(4.76,4.541)(1.19,0.527)(-1.19,-0.527)o