![]() ![]() Same thing as the slope of tangent line, slope And they say at t equals seven, it's equal to negative three. With respect to time, that's going to give you v prime, and these are all functions of t. ![]() Line to the graph of v, that's just v prime. And so they're talking about the slope of the tangent line to the graph, the slope of the tangent Volume is in liters,Īnd time is in minutes. Write out that interpretation, make sure to get the units right. So pause this video again and try to do what we justĭid with the previous example. What is the best interpretationįor the following statement? The slope of the line tangent to the graph of v at t equals seven isĮqual to negative three. Volume of liquid in the tank, in liters, after t minutes. This is 100 kilometers, kilometers, per hour. Given in kilometers, and now we're gonna be thinking about kilometers per unit time. Drove at an instantaneous, instantaneous, instantaneous rate of, and let me use a differentĬolor now for this part, of 100, and what are the units? Well, the distance was ![]() So two hours after leaving, after leaving, Eddie, Eddie, drove, drove, and this means, so it'llīe grammatically correct. What is our time now? Well, that is our t, and that's in hours. Of two is equal to 100, that would mean, well, So we could view this as d prime is going to give you the instantaneous, instantaneous, instantaneous rate. So one way to think about it is, it is the rate of change of d. If d is equal to the distance, the distance driven, then to get d prime, you're taking the derivative What do you think this means, and be sure to include So pause this video, and IĮncourage you to write it out. What is the best interpretationįor the following statement? D prime of two is equal to 100. The function d gives the total distance Eddie has driven in kilometers t hours after he left. We are told that Eddie drove from New York City to Philadelphia. ![]()
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