If {{MATH_111}} for all {{MATH_112}} in an interval {{MATH_113}}, then {{MATH_114}} is constant on {{MATH_115}}. {{CMD_116}} Let {{MATH_117}} be two points in {{MATH_118}}. Since {{MATH_119}} is continuous on {{MATH_120}} and differentiable on {{MATH_121}}, by the Mean Value Theorem we know {{MATH_122}} for some {{MATH_123}} in the interval {{MATH_124}}. Since {{MATH_125}} we see that {{MATH_126}}. {{COMMENT_127}} Moreover, since {{MATH_128}} and {{MATH_129}} were arbitrarily chosen, {{MATH_130}} must be the constant function. {{CMD_131}} {{CMD_132}}