Consider the following accumulation function for {{MATH_97}}. {{MATH_98}} Where is {{MATH_99}} increasing? Where is {{MATH_100}} decreasing? When does {{MATH_101}} have local extrema? {{CMD_102}} From our previous example, we know that {{MATH_103}} is increasing on {{MATH_104}}. Since {{MATH_105}} continues to be positive at {{MATH_106}} and beyond, {{MATH_107}} is {{CMD_108}}{{CMD_109}}increasing{{CMD_110}}{{CMD_111}}decreasing{{CMD_112}}{{CMD_113}} on {{MATH_114}}. On the other hand, we know from our previous example that {{MATH_115}} is {{CMD_116}}{{CMD_117}}increasing{{CMD_118}}{{CMD_119}}decreasing{{CMD_120}}{{CMD_121}} on {{MATH_122}}. {{CMD_123}} {{ENV_124}} {{COMMENT_125}} {{COMMENT_126}} {{CMD_127}} For values to the left of {{MATH_128}}, {{MATH_129}} is still decreasing, as less and less positively signed area is accumulated. Hence {{MATH_130}} is increasing on {{MATH_131}}, decreasing on {{MATH_132}} and hence has an absolute minimum at {{MATH_133}}. {{CMD_134}} {{CMD_135}} The key point to take from these examples is that an accumulation function {{MATH_136}} is increasing precisely when {{MATH_137}} is positive and is decreasing precisely when {{MATH_138}} is negative. In short, it seems that {{MATH_139}} is behaving in a similar fashion to {{MATH_140}}.