Explain why the graphs of the functions {{MATH_96}} and {{MATH_97}} intersect on the interval {{MATH_98}}. {{CMD_99}} To start, note that both {{MATH_100}} and {{MATH_101}} are continuous functions on the interval {{MATH_102}}, and hence {{MATH_103}} is also a continuous function on the interval {{MATH_104}}. Now {{ENV_105}} and in a similar fashion {{ENV_106}} Since {{MATH_107}} and {{MATH_108}} we see that the expression above is positive. Therefore, {{MATH_109}}, and by the Intermediate Value Theorem, there exist a number {{MATH_110}} in {{MATH_111}} such that {{MATH_112}} But this means that {{MATH_113}} and that {{MATH_114}}. Therefore, the curves {{MATH_115}} and {{MATH_116}} intersect at the point {{MATH_117}}. {{CMD_118}} We can see this point of intersection by looking at the graphs of {{MATH_119}} and {{MATH_120}} on the given interval. {{MATH_121}} {{CMD_122}} {{CMD_123}} {{CMD_124}}