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# Use the guidelines of this section to sketch the curve.$y = x + \cos x$

## see graph

Derivatives

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So we know the domain for this one is X is all really And for intercepts 01 there is no symmetry and there's no Assen totes. Let's find the first derivative. So why prime equals one minus sign X. So if we said the first derivative equal to zero, we can find critical points at every pie over too. Plus two pi n. So if you make a cluck for a crime, this is our first derivative test. So this is pi over too. So we're just gonna do one period so positive? Positive? All right, so it's not a man or a Max. We're going to see an inflection here and now I'm gonna solve for the second derivative. So why Double prime equals negative co sign of X. And if he said that equal to zero, we see exit every pie over too, plus pi n. And if we draw the line for this double crime, if this is pi over too, and this is three pi over too negative, positive, negative. So over here, it's gonna be con cave down here. It's gonna become gave up here. It's gonna be con cave. So let's try to grab it. Actually, let's, um since we're just gonna do one period, let's make it all Premier Li. Right. So over here we have Hi. Over here we have two pi, so that means here is through pi over two. And here's pi over too. All right. And we said that we haven't intercept at 01 So let's say this is one. This is our intercept, the Y axis. Next we see that there is a switch from Con Cave down to con Cave up at Pi over too. So this is pi over too. So it started Kong cave down and then the second and got two pi over to its switched concave up. It's gonna keep going Con cave up until about three pi over to then it's gonna go back your pie over two. And now it's gonna start to go back to Con Cave down until we get to the next pi over too. Plus two where it will then. But for the period that we have, it's right here. So from here to here, this is one period

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