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Unformatted text preview: RATES OF CHANGE IN NATURAL AND SOCIAL SCIENCES Example 1. Suppose that C ( s ) gives the number of calories that an average adult burns by walking at a steady speed of s miles per hour for one hour. (1) What are the units of dC ds ? Solution Because C is measured in calories s is in mph , the units of dC ds is ( cal/mph ). (2) Do you expect dC ds to be positive? Why or why not? Solution We can expect dC ds to be positive, because more calories will be burned as we increase the speed. (3) Interpret the statement C (3) = 25. Solution At the speed of 3 mph, if we increase the walking speed by s mph, 25 s more calories will be burned. Example 2. When we consider the flow of blood through a blood vessel, we can model the shape of blood vessel by a cylindrical tube with radius R and length l . Because of friction at the walls of the tube, the velocity v of the blood is greatest along the central axis of the tube and decreases as the distance r from the axis increases. The relationship betweenincreases....
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- Fall '09