函數(shù)y=(13x+2)2(8x-7)的主要性質(zhì)及其圖像主要內(nèi)容：通過函數(shù)的定義域、值域、單調(diào)性、凸凹性及極限的性質(zhì)，并通過函數(shù)導(dǎo)數(shù)知識(shí)求解函數(shù)的單調(diào)區(qū)間和凸凹區(qū)間，并簡(jiǎn)要畫出函數(shù)y=(13x+2)2(8x-7)示意圖的過程與步驟?！?函數(shù)定義域根據(jù)函y=(13x+2)2(8x-7)特征，可知函數(shù)自變量x可以取全體實(shí)數(shù)，即函數(shù)的定義域?yàn)椋海?∞，+∞）?！?函數(shù)的單調(diào)性：本處通過導(dǎo)數(shù)工具來解析函數(shù)的單調(diào)性，過程如下：∵y=(13x+2)2(8x-7)，∴y'=26(13x+2)(8x-7)+(13x+2)2*8，=(13x+2)[26(8x-7)+8(13x+2)]=(13x+2)(312x-166)。令y'=0，有13x+2=0，312x-166=0，即：x1=-eq\f(2,13)≈-0.15，x2=-eq\f(-166,312)≈0.53.(1).當(dāng)x∈(-∞，-0.15)，(0.53,+∞)時(shí)，eq\f(dy,dx)>0,函數(shù)為增函數(shù)。(2).當(dāng)x∈[-0.15，0.53]時(shí)，eq\f(dy,dx)<0,此時(shí)函數(shù)為減函數(shù)?！?函數(shù)的凸凹性∵y'=(13x+2)(312x-166)∴y''=13(312x-166)+312(13x+2)=26(312x-59).令y''=0，則312x-59=0，即：x=eq\f(59,312)≈0.19。此時(shí)函數(shù)的凸凹性及凸凹區(qū)間為：(1)當(dāng)x∈(-∞,0.19)時(shí)，y''<0,此時(shí)函數(shù)y為凸函數(shù)。(2)當(dāng)x∈[0.19,+∞)時(shí)，y''>0,此時(shí)函數(shù)y為凹函數(shù)?！?函數(shù)的極限lim(x→-∞)(13x+2)2(8x-7)=-∞，lim(x→-EQ\F(2,13))(13x+2)2(8x-7)=0，lim(x→EQ\F(7,8))(13x+2)2(8x-7)=0，lim(x→+∞)(13x+2)2(8x-7)=+∞?！?.函數(shù)的部分點(diǎn)圖x-0.32-0.150.020.190.360.530.70(13x+2)24.705.120.044.679.0123.2(8x-7)-9.6-8.2-6.8-5.5-4.1-2.8-1.4y-45.10-34.7-110.0-182.9-221.2-172.5※.函數(shù)的示意圖yy=(13x+2)2(8x-7)(-0.15,0)(0.02,-34.7)(-0.32,-45.1)(0.19,-110.0)(0.36,-182.9)(