Find the {{MATH_43}}-coordinate of the point where the function {{MATH_44}} has a global minimum. {{CMD_45}} {{MATH_46}} {{CMD_47}} Observe that {{MATH_48}} for all {{MATH_49}} in the domain of {{MATH_50}}. Notice that the function {{MATH_51}} does not have a local minimum at {{MATH_52}}. Recall, a function cannot not have a local extremum at a boundary point. {{CMD_53}} {{CMD_54}} {{COMMENT_55}} Find the {{MATH_56}}-coordinate(s) of the point(s) where the function {{MATH_57}} has a local minimum. {{CMD_58}} {{MATH_59}} {{CMD_60}} Observe that {{MATH_61}} for all {{MATH_62}} in the interval, say, {{MATH_63}}. But it is not true that {{MATH_64}} for all {{MATH_65}} in the domain of {{MATH_66}}. For example, {{MATH_67}}. {{CMD_68}} {{CMD_69}} {{CMD_70}} Does every function attain a global extremum on its domain? Select the correct answer. {{CMD_71}} {{CMD_72}}All functions must attain both global minimum and global maximum on their domain.{{CMD_73}} {{CMD_74}}All functions attain a global minimum on their domain.{{CMD_75}} {{CMD_76}}All functions attain a global maximum on their domain.{{CMD_77}} {{CMD_78}}Some functions have no global extremums on their domain.{{CMD_79}} {{CMD_80}} {{CMD_81}} Check the following graph. {{CMD_82}} {{ENV_83}} {{CMD_84}} Notice, the function is {{CMD_85}}not continuous{{CMD_86}} at {{MATH_87}}, and, therefore, {{MATH_88}} is {{CMD_89}}not continuous{{CMD_90}} on its domain, {{MATH_91}}.{{CMD_92}} Does the function given by the graph above attain a global extremum on its domain? Select the correct answer. {{CMD_93}} {{COMMENT_94}}