所给函数的定义域为[tex=7.857x1.286]NIBUWATaDP1vuLO1XdxO9fliQGMsENMf3eZZbcwDClwQB/mVuUHLZvxzD1b4voOO[/tex]，[tex=6.214x2.357]4AuFSHIlRNBYGYNGbRhVOX6vTVLBTGyXySmX8c5tJcNlti2o+eZQo0/FV5NMPjWd[/tex]，令[tex=2.571x1.286]cIcAGLCbWpT5vpeiB6BdKVEXMySzhw2VjsXRyMdnHCc=[/tex]，得驻点[tex=2.357x1.286]F20DA9b5PZyvxJH27l4LOQ==[/tex]及[tex=2.357x1.286]+1uQITH0WA9VdOa9Vpywhg==[/tex]，[tex=5.929x2.214]Ei2PZQl92La73hUrygebc8rDE8M+lEmtxrMw6nHE9PNadnwucg5YY3hni7iH+coz[/tex]，令[tex=2.786x1.286]Ei2PZQl92La73hUrygebc2+D1m3XSs3rxM2JO1NI0o4=[/tex]，得[tex=2.357x1.286]F20DA9b5PZyvxJH27l4LOQ==[/tex]。列表讨论如下：[img=928x232]177b32a7c8b419c.png[/img]由此可知：（1）函数的单调增加区间为[tex=3.357x1.286]Fx7eEsKBKHtGT5KmhKIQ0sGhGQBhgLJeZ3bhDxMqR2A=[/tex]和[tex=3.357x1.286]rgcLoTflTL5Oa6xDzkGCBusBvxGx+srp7QOd/nPv9S0=[/tex]，单调减少区间为[tex=2.143x1.286]1FU1/J8bvECZ5AYU6Nzzkw==[/tex]；极小值为[tex=4.857x2.0]HcVZp5W0l7gxqJgKxGmkqHEC54yZKdL+4ScLAMCWG+uXbXZnbIQ72CzRIL85BhWm[/tex]。（2）函数图形在区间[tex=3.357x1.286]GO2Q4a32nZmeZIdzbMswF6W+TEgdE15g98VUZ7PDeN8=[/tex]内是凹的，在区间[tex=2.143x1.286]VykF7BpO3NFT550xU7Tx1w==[/tex]，[tex=3.357x1.286]UkaN5FTDX8NstSc/rak5hyQV52XkF76w6KzuciSX8to=[/tex]内是凹的，拐点为点[tex=2.143x1.286]q8d9ecMZwZI3gbdeOe+7AA==[/tex]。（3）由[tex=8.429x2.357]MqOfsQLAB/zeVSdv1WggGKZwlfqkl5pMpw5gm9O7BZhHEmUpTPAU3njabSknJiL5tDePM+j7apyGvJal6WCbZw==[/tex]知，[tex=2.357x1.286]jgIRiGqlkdCMqO92sJAASg==[/tex]是函数图形的铅直渐近线；又[tex=4.0x1.786]MqOfsQLAB/zeVSdv1WggGGNA1nanMzinW5TtkpbVmmVXWO6o1I48WrHgHgyq5/iK[/tex][tex=7.571x2.357]MqOfsQLAB/zeVSdv1WggGGNA1nanMzinW5TtkpbVmmWKiHeL8APebhZYhkzLfjlZ5I0AnAnZ1i8eCjqLegwYxQ==[/tex]，[tex=6.0x1.571]MqOfsQLAB/zeVSdv1WggGNhc4+cPMzaQkdv5GwZF7uas1cQUGPzzr/KwuH+sFEQ+[/tex][tex=10.357x2.357]MqOfsQLAB/zeVSdv1WggGJzD8FlSPdx/+VJ1FKsc1mTxHMrWzvOfospdVwPJc0V1s1/Ic4p87esAVBu5B2Yx8t8GA2CLuEisUlaSV3gGViE=[/tex]，故[tex=4.071x1.286]6hxHeYAmLyLkooWhSZ02zw==[/tex]是函数图形的斜渐近线。