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$59-62$ Produce graphs of $f$ that reveal all the important aspectsof the curve. In particular, you should use graphs of $f^{\prime}$ and $f^{\prime \prime}$ toestimate the intervals of increase and decrease, extreme values,intervals of concavity, and inflection points.$$f(x)=\tan x+5 \cos x$$

We used the concept of first and second differentiation to solve this. Check inside for more details. Please note that this is a periodic function with a period of 2$\pi .$ So we can have multiple intervals a multiple inflection, maximum, minimum points.

Calculus 1 / AB

Chapter 4

Applications of Derivatives

Section 2

How Derivatives Affect the Shape of a Graph

Differentiation

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University of Michigan - Ann Arbor

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Lectures

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In mathematics, precalculu…

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In mathematics, a function…

$59-62$ Produce graphs of …

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Produce graphs of $ f $ th…

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07:48

11:23

09:48

09:01

07:20

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In Exercises 63-70, use th…

his clothes when you read here, So theory ever function Original one 10 minutes is plus five co sign. That's now we're gonna draw this graph. Go something like this, and I'll just continue to look at that throughout and are first derivative ISS seek it. Square minus five. Signed X and I look something like this. Mmm. And then our last graph looks into this. No, We're gonna go back to our original graph, and we see that the function is increasing from negative three point negative. Three pi over too. Coleman to get a 4.215 and negative. 3.352 common negative by half and negative pie half calm. A point 211 and 1.0. So for call up, I have for decreasing what inside? Negative. 4.21 Fly common Negative. 3.352 in 0.211 Come on. 1.74 The local maximum value issue negative. 5.103 And this is that when X equals negative 3.352 and 4.228 That access equal to 1.74 and the local maximum volume issue, you could have 4.22 feet X is equal to negative 4.215 and five point ones, or three X is equal to 0.211 for a second function because see that the changes sign at the values Max equals negative. 4.21 looks 15 negative 3.3 front too, 0.211 at one point, Sara A 74 and it goes from positive to negative when it's negative. 3.352 in 1.0 sum. For then, these are local minimum on local maximum. Our next equals make it a 4.215 and 0.211 for a final graph. We see that this one changes. Sign that negative 3.9 Zahra Tune 0.76 So these are going to be inflection points and the changes from negative to positive. So it goes from calling Cape down to call Kate

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In mathematics, precalculus is the study of functions (as opposed to calculu…

In mathematics, a function (or map) f from a set X to a set Y is a rule whic…

$59-62$ Produce graphs of $f$ that reveal all the important aspectsof th…

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Evaluate the integral.$\int_{0}^{1} \frac{4}{t^{2}+1} d t$

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Find $f$ . $f^{\prime}(x)=\sqrt{x}(6+5 x), \quad f(1)=10$

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Find $d y / d x$ by implicit differentiation.$e^{x / y}=x-y$

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