The water level, measured in feet above mean sea level, of Lake Lanier in Georgia, USA, during 2012 can be modeled by the function L(t) = 0.01441t 3 − 0.4177t 2 + 2.703t + 1060.1 where t is measured in months since January 1, 2012. Estimate when the water level was highest during 2012.

May 4th, 2012.

Step-by-step explanation:

The highest level can be found with the help of the First Derivative and Second Derivative Tests. First and second derivatives of the function are, respectively:

The First Derivative Tests consists on equalizing the first derivative to zero and finding the critical points.

Roots are and . just the second root offer a realistic solution and is test by the second derivative.

(which leads to a maximum).

Given that a year has 365 days or 12 months, the highest water level occurs at day:

(May 4th).