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Unformatted text preview: Math 1a: Lecture 2
September 11, 2009
1. The following are some odometer readings during my bike ride to Harvard: Time (hh:mm) Distance (meters) 10:00 0 10:01 610 10:02 980 10:04 1240 10:05 1250 10:06 1260 10:08 1520 10:09 1890 10:10 2500 (a) What was my average speed for the ride? (b) What was my average speed for the first two minutes? What about the middle two minutes (10:04 to 10:06)? (c) My advisor saw me a minute before I reached Harvard. According to him, I was going dangerously fast. Can we give some estimates for how fast I was going when he saw me? (d) I showed this data to my friend Isaac and he realized that it can be described exactly by the function f (x) = 10(x - 5)3 + 1250, where f (x) is the distance I had travelled (in meters) until time x (in minutes). Assuming he is right, can we better estimate my instantaneous speed at 10:09? Can we guess the exact value of the instantaneous speed? 1 2. Consider the function f (x) = 3x2 + 1. (a) Draw a rough sketch of the graph of f . (b) Find k so that the graph passes through the point P = (1, k). (c) Approximate the slope of the tangent line to f at P by computing the slope of some nearby secants. (d) Can we guess the slope of the tangent line at P ? Use this guess to write the equation of the tangent line to the graph of f at P . 2 ...
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This note was uploaded on 03/27/2012 for the course MATH 1a taught by Professor Benedictgross during the Fall '09 term at Harvard.
- Fall '09