Jim moves along an elevation function:

He starts from 6 feet below sea level and end at 100 feet above sea level. When will he pass through sea level? The unit for distance is feet and the unit for time is minute.

First set up coordinate system based on s and t and plot the function. In the diagram:

• The elevation change is continuous when t > 0.
• He starts from 6 feet below sea leavel (s = -6) and finishes 100 feet above (s = 100). Their signs are opposite.

According to corollary of intermediate value theorem,
t² - t - 6 = 0 has at least one root when t > 0.

Solving the equation:

     t² - t - 6 = 0

      (t + 2)(t - 3) = 0

      t = 3       t = -2 (discard, not practical)

Thus, Jim will pass through sea level when t = 3 minutes.