When looking for local maximum and minimum points, be careful not to make two sorts of mistakes: {{CMD_304}} {{CMD_305}} You may forget that a maximum or minimum can occur where the derivative does not exist, and so forget to check whether the derivative exists everywhere. {{CMD_306}} You might assume that any place that the derivative is zero is a local maximum or minimum point, but this is not true, consider the plots of {{MATH_307}} and {{MATH_308}}. {{CMD_309}} {{ENV_310}} {{COMMENT_311}} {{COMMENT_312}} {{COMMENT_313}} {{CMD_314}} While {{MATH_315}}, there is neither a maximum nor minimum at {{MATH_316}}. {{CMD_317}} {{CMD_318}}