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Produce graphs of $f$ that reveal all the importantaspects of the curve. In particular, you should use graphs of $f^{\prime}$and $f^{\prime \prime}$ to estimate the intervals of increase and decrease,extreme values, intervals of concavity, and inflection points.$$f(x)=6 \sin x+\cot x, \quad-\pi \leqslant x \leqslant \pi$$

$f(-0.773)=-5.22, f(0.773)=5.22$

Calculus 1 / AB

Chapter 4

APPLICATIONS OF DIFFERENTIATION

Section 4

Curve Sketching

Derivatives

Differentiation

Applications of the Derivative

Campbell University

Baylor University

University of Michigan - Ann Arbor

University of Nottingham

Lectures

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mhm So this craft we're going to produce and we're going to analyze it in the context of the derivative graphs. So, the one that we're focused on for this problem is six sine of X plus Code Canyon X. So let's look at that graph and it's going to be from negative pi Hi, Okay. So let's look at that graph and see it looks like this interestingly shaped graph. But it'll make more sense when we look at the derivative function. So you see that the graph overall is decreasing here until it reaches this value right there. Once again, the graph according to the derivative graph is decreasing until it reaches this value right here, which is why this is a local minimum. Then the graph increases until it reaches this value right here, Point- .444. At that point the graph starts decreasing, which is why the derivative graph goes negative. Then we see the graph breaks and it starts off here starting off and it's going to be decreasing as it does here, then it reaches zero value, which corresponds to that local minimum .444. It increases until it reaches this point, similarly shown here, and then the graph decreases to infinity. And that's shown in the derivative graph as well. Then we look at the second derivative graph Furqan cavity, we see the graph is concave up all the way up until here, which is why it's shown that up until actually more like here, the grafters can came up, then it goes concave down at that inflection point, which is why it's opening down like this and that's why it goes negative. Then this graph, this portion of the graph right here is concave up until it reaches its inflection point. Um And we see that it's concave up and then it goes concave down and that is for the entirety or the rest of the graph. That is

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