The temperature on venus: The air temperature one balmy summer evening at your summer resort near Maxwell Montes, t hours after 5:00 pm, was given by the function
What was the temperature at 8:00 pm, and how fast was it dropping?
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In cold climates, including the northern United States, a house can be built with very large windows facing south to take advantage of solar heating. Sunlight shining in during the daytime is absorbed by the floor, interior walls, and objects in the room, rasing their temperature to 38.0 degrees C. If the house is well insulated, you may model it as losing energy by heat steadily at the rate 6000 W on a day in April when the average exterior temperature is 4 degrees C and when the conventional heating system is not used at all. During the period between 5:00 PM and 7:00 AM, the temperature of the house drops and a sufficiently large "thermal mass" is required to keep it from dropping too far. The thermal mass can be a large quantity of stone (with specific heat 850 J/kg*C) in the floor and the interior walls exposed to sunlight. What mass of stone is required if the temperature is not to drop below 18.0 degrees C overnight?)
Average Speed of a Highway Vehicle The average speed of a vehicle on a stretch of Route 134 between 6 A.M. and 10 A.M. on a typical weekday is approximated by the function
where f (t) is measured in miles per hour and t is measured in hours, with t = 0 corresponding to 6 A.M.
(a) Compute f'(t)
(b) What is the average speed of a vehicle on that stretch of route 134 at 6:00 AM? 7:00 AM? 8:00 AM?
(c) How fast is the average speed of a vehicle on that stretch of route 134 changing at 6:30 AM? 7:00 AM? 8:00 AM?
