The temperature in the City of Monterrey on a summer day is modeled by the equation in the photo. Where T is given in Celsius and t in hours from midnight. a)Describe the behavior of temperature as a function of time. b)Find the rate of change in temperature as a function of time. c)Graph T(t) and T′(t) in the same plane and compare them to answer: At what time of day is the temperature lowest and at what time is it highest? What happens to the rate of change at that time?
The temperature in the City of Monterrey on a summer day is modeled by the equation in the photo. Where T is given in Celsius and t in hours from midnight.
a)Describe the behavior of temperature as a function of time.
b)Find the rate of change in temperature as a function of time.
c)Graph T(t) and T′(t) in the same plane and compare them to answer: At what time of day is the temperature lowest and at what time is it highest? What happens to the rate of change at that time?
A graph is a graph of a function if it satisfies the vertical line test.
That is, each vertical line must touch the graph exactly at one point.
A graph is increasing when the rate of change or the derivative of the function is positive.
A graph is decreasing if the rate of change or the derivative of the function is negative.
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