First, compute {{MATH_63}} {{CMD_64}} The function {{MATH_65}} has {{MATH_66}} critical point(s). {{CMD_67}} The single critical point of {{MATH_68}} is located at {{MATH_69}} {{CMD_70}} Now compute {{MATH_71}} {{CMD_72}} Because the value of {{MATH_73}} is {{CMD_74}}{{CMD_75}}positive{{CMD_76}}{{CMD_77}}negative{{CMD_78}}{{CMD_79}}zero{{CMD_80}}{{CMD_81}}, the local extremum {{MATH_82}} has at {{MATH_83}} is {{CMD_84}}{{CMD_85}}a local maximum{{CMD_86}}{{CMD_87}}a local minimum{{CMD_88}}{{CMD_89}}neither a local maximum nor a local minimum{{CMD_90}}{{CMD_91}}possibly a local maximum, a local minimum or neither{{CMD_92}}{{CMD_93}} by the second derivative test. {{CMD_94}} Since {{MATH_95}} is decreasing on the interval {{MATH_96}} and is increasing on the interval {{MATH_97}}, {{MATH_98}} has {{CMD_99}}{{CMD_100}}no global minimum{{CMD_101}}{{CMD_102}}a global minimum{{CMD_103}}{{CMD_104}} at {{MATH_105}}. The global minimum of {{MATH_106}} is {{MATH_107}}. {{CMD_108}} On the other hand, the function {{MATH_109}} is {{CMD_110}} {{CMD_111}}increasing on {{MATH_112}}{{CMD_113}} {{CMD_114}}decreasing on {{MATH_115}}{{CMD_116}} {{CMD_117}}increasing on {{MATH_118}} and decreasing on {{MATH_119}}{{CMD_120}} {{CMD_121}}decreasing on {{MATH_122}} and increasing on {{MATH_123}}{{CMD_124}} {{CMD_125}} {{CMD_126}} Since {{MATH_127}} is increasing on {{MATH_128}} and since {{MATH_129}}, it follows that for all {{MATH_130}}, {{MATH_131}} {{CMD_132}} Therefore on {{MATH_133}}, {{MATH_134}} is positive and {{CMD_135}}{{CMD_136}}bounded{{CMD_137}}{{CMD_138}}unbounded{{CMD_139}}{{CMD_140}}. Therefore {{MATH_141}} {{CMD_142}}{{CMD_143}}has a global maximum{{CMD_144}}{{CMD_145}}has no global maximum, but does have a local maximum{{CMD_146}}{{CMD_147}}has no global maximum{{CMD_148}}{{CMD_149}}has no global maximum, but may have a local maximum{{CMD_150}}{{CMD_151}}. {{CMD_152}} Finally, we shall identify the inflection points of {{MATH_153}} and the intervals on which {{MATH_154}} is concave up or concave down.