微积分求Concave up和Concave down

研究函数f(x)=ln(11x²+2)的凹凸性,并求出其垂直和水平的渐近线.
f'(x)=22x/(11x²+2)；
令f''(x)=[22(11x²+2)-484x²]/(11x²+2)²=(-242x²+44)/(11x²+2)²=-(242x²-44)/(11x²+2)²
=-[11(√2)x+2√11][11(√2)x-2√11]/(11x²+2)²=0
得得拐点x₁=-(2/11)√(11/2)=-(1/11)√22；x₂=(1/11)√22；
当x<-(1/11)√22或x>(1/11)√22时f''(x)<0；即在区间(-∞,-(1/11)√22]∪[(1/11)√22,+∞)内曲线向下
凹【即向上凸】；当-(1/11)√22]0,即在区间[-(1/11)√22,(1/11)√22]
内曲线向上凹【即向下凸】.
既无水平渐近线,也无垂直渐近线.其图像如下：