Chapter 7 Differential Calculus Section 7.6 Final Test
7.6.1 Final Test Module 7This is a test for submission:
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In a container at 9 a.m. a temperature of is measured. At 3 p.m. the measured temperature is . After a period of 14 hours, the temperature has fallen to .
- What is the average rate of temperature change between the first and second measurements?
- The `falling' property of the temperature shows in the fact that the rate of change is
- Calculate the average rate of temperature change for the whole measuring period.
Calculate for the function
- with the value of the first derivative at :
- with the value of the second derivative at :
Consider the function , with . On which regions is monotonically decreasing, and on which regions is concave? Specify the regions as open intervals that are as large as possible:
- is monotonically decreasing on .
- is concave on .
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