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02-tangents-velocities

02-tangents-velocities - Math 1a Velocities Secants&...

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Unformatted text preview: Math 1a Velocities, Secants & Tangents Fall, 2009 1 My father lives a two-and-a-half hour (150 minute) drive away. On a recent trip to visit him I recorded the trip odometer at regular intervals: Time (minutes) 30 60 90 120 150 Distance (km) 30 80 135 185 205 (a) What was my average speed for the trip? (b) What was my average speed for the first half hour of the trip? (c) How fast was I going exactly two hours into the trip? That is, what was my speedometer reading at time 120 minutes? Explain your reasoning. (d) Repeat the previous problem at two-and-a-half hours into the trip. Is your estimate too high or too low? Why? 2 It turns out my odometer records the mileage (kilometrage?) every 2 minutes, so in fact we can re-write the end of the table in the previous problem as Time (minutes) 146 148 150 Distance (km) 202 . 5 204 205 Use this information to estimate my speed at 150 minutes. Is this estimate too high or too low? 3 Let f ( x ) = 1 /x . (a) Is the slope of the tangent line to f at P = (1 / 2 , 2) positive or negative? (b) Estimate the slope of the tangent line to f at P by computing the slope of a secant line through P and Q = (0 . 49 ,f (0 . 49)). (c) Can you guess the exact slope of the tangent line at P ? (d) What is the equation of the tangent line to f at P ? 4 The graph below shows the plot of a function y = f ( x ). ......................................................................................................................................................................................................................................................... . . . . . . . . . . . . 1 2 3 4 5 6 7 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 3 4 5 ....
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