It goes as high as 240. But what we could do is, and this is essentially what we did in this problem. We can estimate v prime of 16 by thinking about what is our change in velocity over our change in time around 16. Voiceover] Johanna jogs along a straight path. This is how fast the velocity is changing with respect to time. AP CALCULUS AB/CALCULUS BC 2015 SCORING GUIDELINES Question 3 t (minutes) v(t)(meters per minute)0122024400200240220150Johanna jogs along a straight path. So, let's say this is y is equal to v of t. And we see that v of t goes as low as -220. Johanna jogs along a straight path lyrics. So, if you draw a line there, and you say, alright, well, v of 16, or v prime of 16, I should say. And we would be done.
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So, -220 might be right over there. So, this is our rate. And we see on the t axis, our highest value is 40. And so, this would be 10.
Johanna Jogs Along A Straight Path. For
But this is going to be zero. And so, these are just sample points from her velocity function. So, 24 is gonna be roughly over here. They give us when time is 12, our velocity is 200.
Johanna Jogs Along A Straight Pathologie
And we see here, they don't even give us v of 16, so how do we think about v prime of 16. Well, just remind ourselves, this is the rate of change of v with respect to time when time is equal to 16. And when we look at it over here, they don't give us v of 16, but they give us v of 12. We see that right over there. They give us v of 20.
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For good measure, it's good to put the units there. When our time is 20, our velocity is going to be 240. Use the data in the table to estimate the value of not v of 16 but v prime of 16. We could say, alright, well, we can approximate with the function might do by roughly drawing a line here. Fill & Sign Online, Print, Email, Fax, or Download. So, we could write this as meters per minute squared, per minute, meters per minute squared. Johanna jogs along a straight pathologies. So, at 40, it's positive 150. Let me do a little bit to the right. So, let me give, so I want to draw the horizontal axis some place around here. So, when the time is 12, which is right over there, our velocity is going to be 200.
That's going to be our best job based on the data that they have given us of estimating the value of v prime of 16. So, that's that point. And so, let's just make, let's make this, let's make that 200 and, let's make that 300. So, our change in velocity, that's going to be v of 20, minus v of 12. So, that is right over there. So, we literally just did change in v, which is that one, delta v over change in t over delta t to get the slope of this line, which was our best approximation for the derivative when t is equal to 16. For 0 t 40, Johanna's velocity is given by. We see right there is 200. And so, this is going to be equal to v of 20 is 240. But what we wanted to do is we wanted to find in this problem, we want to say, okay, when t is equal to 16, when t is equal to 16, what is the rate of change? Johanna jogs along a straight pathologie. For zero is less than or equal to t is less than or equal to 40, Johanna's velocity is given by a differentiable function v. Selected values of v of t, where t is measured in minutes and v of t is measured in meters per minute, are given in the table above. So, we can estimate it, and that's the key word here, estimate. And so, these obviously aren't at the same scale. Well, let's just try to graph.
Let's graph these points here. If we put 40 here, and then if we put 20 in-between. So, she switched directions. And so, what points do they give us? And then, finally, when time is 40, her velocity is 150, positive 150. We go between zero and 40.
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