   Chapter 3.1, Problem 65E

Chapter
Section
Textbook Problem

# 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 )   = 0.0144 t 3 −   0.4177 t 2 +   2.703 t   +   1060.1 where t is measured in months since January 1, 2012. Estimate when the water level was highest during 2012.

To determine

To estimate:

When the water level was the highest during 2012.

Explanation

1) Concept:

Use the Closed Interval Method to estimate when the water level was the highest during 2012.

The Closed Interval Method:

To find the absolute maximum and minimum values of a continuous function f on a closed interval a, b:

i. Find the values of f at the critical numbers of f in a, b

ii. Find the values of f at the end points of the interval

iii. The largest of the values from step (i) and (ii) is the absolute maximum value; the smallest of these values is the absolute minimum value.

2) Given:

Lt=0.01441t3-0.4177t2+2.703t1+1060.1

t is measured in months

3) Calculation:

Since t is measured in months, use the interval as 0, 12.

Differentiate Lt with respect to t by using the power rule of derivative.

L'(t)=0.04323t2-0.8354t+2.703

Now set L'(t)=0, and solve for t.

t=-b±b2-4ac2a

=0

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