函數(shù)y=eq\f(3,x(86x2-2))的圖像示意圖主要內(nèi)容：介紹分?jǐn)?shù)函數(shù)y=eq\f(3,x(86x2-2))的定義域、值域、單調(diào)性、凸凹性、極限等主要函數(shù)性質(zhì)，并通過導(dǎo)數(shù)知識求解計算函數(shù)的單調(diào)區(qū)間和凸凹區(qū)間，綜合函數(shù)性質(zhì)畫出該函數(shù)圖像的示意圖。函數(shù)定義域：因為y=eq\f(3,x(86x2-2))，所以分母不為0，觀察分母函數(shù)特征，可知自變量x不為0，且86x2-2≠0，即x2≠eq\f(1,43)，則x1≠-eq\r(eq\f(1,43))≈-0.15，x2≠eq\r(eq\f(1,43))≈0.15。所以函數(shù)的定義域為(-∞，-0.15)，(-0.15，0)，(0，0.15)，(0.15，+∞)。由于函數(shù)的分子為1，所有該函數(shù)y≠0，故函數(shù)的值域為(-∞，0),(0，+∞）。函數(shù)的單調(diào)性：由y=eq\f(3,x(86x2-2))，對x求導(dǎo)得：eq\f(dy,dx)=-3*eq\f((86x2-2)+x*172x,[x(86x2-2)]2)=-3*eq\f(258x2-2,[x(86x2-2)]2),令eq\f(dy,dx)=0,則258x2-2=0，此時有：x3=-eq\r(\f(1,129))≈-0.09，x4=eq\r(\f(1,129))≈0.09。所以函數(shù)的單調(diào)性及單調(diào)區(qū)間為：(1)當(dāng)x∈(-∞，-0.15)，(-0.15，-0.09]，[0.09，0.15)，(0.15，+∞)時，eq\f(dy,dx)>0,函數(shù)為增函數(shù)。(2)當(dāng)x∈(-0.09，0)，(0，0.09）時，eq\f(dy,dx)<0,函數(shù)為減函數(shù)。函數(shù)的凸凹性：由eq\f(dy,dx)=-3*eq\f(258x2-2,[x(86x2-2)]2)，再次對x求導(dǎo)得，eq\f(d2y,dx2)=-3*eq\f(516x[x(86x2-2)]2-2(258x2-2)[x(86x2-2)](86x2-2+172x2),[x(86x2-2)]4)=-3*eq\f(516x2(86x2-2)-2(258x2-2)(258x2-2),[x(86x2-2)]3)=3*eq\f(2[258x2(86x2-2)-(258x2-2)2],[x(86x2-2)]3)=3*eq\f(8(11094x4-129x2+1),[x(86x2-2)]3),對于g(x)=11094x4-129x2+1看做x2的二次函數(shù)，判別式=1292-4*11094*1<0,即分子為正數(shù)，所以eq\f(d2y,dx2)的符號取決于分母。(1)當(dāng)x∈(-0.15，0)，(0，0.15)時，eq\f(d2y,dx2)>0，函數(shù)y為凹函數(shù)；(2)當(dāng)x∈(-∞，-0.15)，(0.15，+∞)時，eq\f(d2y,dx2)<0,此時函數(shù)y為凸函數(shù)。函數(shù)的極限:lim(x→-∞)eq\f(3,x(86x2-2))=0，lim(x→0-)eq\f(3,x(86x2-2))=-∞，lim(x→0+)eq\f(3,x(86x2-2))=+∞，lim(x→+∞)eq\f(3,x(86x2-2))=0，lim(x→-0.15-)eq\f(3,x(86x2-2))=-∞，lim(x→-0.15+)eq\f(3,x(86x2-2))=+∞，lim(x→0.15-)eq\f(3,x(86x2-2))=-∞，lim(x→0.15+)eq\f(3,x(86x2-2))=+∞，函數(shù)的奇偶性因為f(x)=eq\f(3,x(86x2-2)),所以f(-x)=eq\f(3,(-x)[86(-x)2-2])，即：f(-x)=-eq\f(3,x(86x2-2))=-f(x).所以函數(shù)為奇函數(shù)，關(guān)于原點對稱。函數(shù)五點圖表x-0.53-0.45-0.38-0.30-0.2386x2-222.215.410.45.72.5y-0.255-0.433-0.759-1.754-5.217x-0.12-0.11-0.09-0.05-0.0486x2-2-0.8-1.0-1.3-1.8-1.9y31.2527.2725.6433.3339.47x0.040.070.090.110.1286x2-2-1.86-1.58-1.30-0.96-0.76y-40.32-27.12-25.64-28.41-32.89x0.230.300.380.450.5386x2-22.55.710.415.422.2y5.2171.7540.7590.4330.255函數(shù)的示意圖f(x)=eq\f(3,x(86x2-2))y(-0.04,39.47)(-0.12,31.25)(-0.09,25.64)(0.23,5.217)（-0.53,-0