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Problem 55 Easy Difficulty

The graph of $ f' $ is shown in the figure. Sketch the graph of $ f $ if $ f $ is continuous on $ [0, 3] $ and $ f(0) = -1 $.

Answer

$F(x)=2 x-1$ in $(0,1)$
$F(x)=x-1$ in $(1,2)$
$F(x)=-x-1$ in $(2,3)$

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Video Transcript

So for this problem were given a prime and we want to sketch the graph um of f if it's continuous on 0 to 3, where fo zero is negative one. Um So we want to show all the different graphs based on what we see in the figure, so we see from 0 to 1, it's going to look like the line two x minus one, and that's from 0 to 1. Uh huh. And then after the second one, we have X. My next one x minus one. And that's going to be from uh one, the two. That's this portion of the graph here. And then lastly, we have from 2 to 3 negative X minus one. So that's gonna look like, is this? And like we said, that's going to be from to western equal to act with less than equal to three. This is going to be our final representation of the graph based on what we're given.