In our next example, we clarify the definition of a local minimum. {{CMD_83}} Consider the graph of a function {{MATH_84}}: {{CMD_85}} {{ENV_86}} {{COMMENT_87}} {{COMMENT_88}} {{CMD_89}} Identify the local extrema of {{MATH_90}} and give an explanation. {{CMD_91}} In the figure above the function {{MATH_92}} has a local minimum at, {{MATH_93}} because we can find an {{CMD_94}}open{{CMD_95}} interval {{MATH_96}} (marked in the figure) that contains the number {{MATH_97}} and for all numbers {{MATH_98}} in {{MATH_99}} the following statement is true: {{MATH_100}} {{CMD_101}} {{CMD_102}}