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Handout Monday 11/10
Today, we might start section 4.1, but more likely we will work some applied optimization problems from section 3.6. Questions from the practice problems would be good, or we can pick a problem from the samples distributed last week.
To start section 4.1:
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At the very beginning of the course, we motivated all of calculus with an example about driving back from DIA. We realized there was a connection between the distance traveled, the time that took, and the velocity of your car.
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In particular, we noted that velocity was given by distance divided by time. Or more precisely, \(v = \frac{\Delta d}{\Delta t}\text{,}\) the change in distance divided by the change in time.
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This allowed us to find the average velocity over any time interval. As that time interval got smaller, we said that these average velocities were essentially the instantaneous velocity. This led us to the definition of a derivative, which we have been studying for the last two months.
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Another question we asked that first day though: if you recorded your speeds every 5 minutes, can you estimate how far you have traveled? We said after 5 minutes, you noticed speeds of 75mph, 60mph, 65mph and 50mph. Or in terms of miles/minute, these numbers are 1.25, 1, 1.08, and 0.84.
