Chapter 4 section 2

Excel Companion Chapter 4 Section 2
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Average and Instantaneous Rates of Change	*TimeTemp.xls*

Open the file TimeTemp.xls. An average rate of temperature change over a time interval from t = a to t = b can be computed as the quotient of two differences: the temperature in Fahrenheit at time b minus temperature at time a divided by the difference b - a.

the slope of the line

between the two points is

TimeTemp.xls-discrete

QUESTIONS:

1.	Find the average rate of change of temperature between 7:00 AM and 9:00 AM.
2.	Find the average rate of change of temperature between 9:00 AM and 1:00 PM.

Associated with each point on the smooth temperature curve is a line called a tangent line. The slope of the tangent line to this curve at a point measures the instantaneous rate of change of the curve at that point. Carefully draw tangent lines to the curve at points that correspond to times of 8:00 AM, 12:00 noon, 2:00 PM, 4:00 PM, and 6:00 PM.

TimeTemp.xls-continuous

Approximate the instantaneous rate of change in questions 3 - 8.
3.	At 8:00 AM the temperature is (increasing/decreasing) at the approximate rate of	degrees/ hour.
4.	At noon the temperature is (increasing/decreasing) at the approximate rate of	degrees/ hour.
5.	At 2:00 PM the temperature is (increasing/decreasing) at the approximate rate of	degrees/ hour.
6.	At 4:00 PM the temperature is (increasing/decreasing) at the approximate rate of	degrees/ hour.
7.	At 6:00 PM the temperature is (increasing/decreasing) at the approximate rate of	degrees/ hour.
8.	At approximately what point in time is the instantaneous rate of change of temperature neither increasing nor decreasing?

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