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Find all the critical number(s) for f (1) = (22 _ 1) e-r_The derivative f' (2) is given below: Use it to answer questions about the function f (2).f' (x) ...

Question

Find all the critical number(s) for f (1) = (22 _ 1) e-r_The derivative f' (2) is given below: Use it to answer questions about the function f (2).f' (x) = ~r(c 2)3 a) Find the intervals on which f is increasing and decreasing: (b) Find the intervals of concavity of the graph of y = f(z)

Find all the critical number(s) for f (1) = (22 _ 1) e-r_ The derivative f' (2) is given below: Use it to answer questions about the function f (2). f' (x) = ~r(c 2)3 a) Find the intervals on which f is increasing and decreasing: (b) Find the intervals of concavity of the graph of y = f(z)



Answers

a. Find the critical points of $f$ on the given interval. b. Determine the absolute extreme values of $f$ on the given interval when they exist. c. Use a graphing utility to confirm your conclusions. $$f(x)=x /\left(x^{2}+1\right)^{2} \text { on } [-2,2]$$

Okay, so it's fine distributed. So we confined our critical points of our fallen function So derivative of X squared. That's two X. Now we'll set that equal to girl and we see that we have a critical point That is excessively to go a new one to also include our endpoints. Since we're looking for absolute men and Max So we had negative too. And X is equal to three. Okay, So plugging in our ex points into are falling function. We yet negative six negative 10 on negative one. So we see that this points here gives us our absolute men, and this gives are absolutely at X is equal to, um great.

I think so. Let's start by finding are critical points. So we take this really centers that we have. Our outermost function is part 1/2 So we'll be using our generals. That's 1/2 exercise two to the power of negative 1/2 times one collects equal to 1/2 times the square root of X minus two on we went to find when this is a girl, Okay, so notice that's we can consider are on the fine points or when our denominator is equal to zero. So that's when accident with two and we'll check our endpoints to So that's executed two and six. And now let's find their corresponding X. So plugging this into my calculator, I get zero. And for six months to two part of one house I get to. So I see that you have, um, on absolute men and this is our absolute max

The function during this question is half off exit. So it's just excess where my Muslim where x belongs to. Okay. For this question, we have to find out what the deployment for maybe a different you. So have less off X will be forced to accept new exists Where my this one minus two x into x square You are needed by excess. Where my missile. Okay, this will be getting on. But this isn't even getting buy just to accept the idea right exists where this one And if your radio for getting is acceptable soup. Okay. And also he introduced the definition of political parties and the first ever girls, you know, for where the function is no different. So you be in seemingly normal that exists where articles to city excess working articles. What do you want? X camera? Because a plus minus one zero minus one of these people. Now we have to check for that check for the experiment using first of your mucus. And for that you do this iteration percentage direction there, this zero. And if you take anybody bar that goes over to be snc the festival, you know, getting and it could be for the positive may be acceptable. Susilo will be that part off extreme. Okay, so just keep your mind off. Okay? Now, entire party. And if I know the Google extreme, so a little extra Max and Leo, therefore, would you? Okay, four minus four four. And if you can t o maximum more four minus four. Everything is 16 and then they don't. So 16 right? AMC global maximum 16. My 15 actually assume minus four.

Pushing your garden. This problem it affects a little su minus X to spend my mistakes. That's to exit strong, minus four. Rueful thus, yes. In the first place, we have to get work. It's creating a point for that. Clearly differentiate your first every day off there minus two x minus one in the nusra zero. Who could do you a YouTube video? So the big, big government getting its excellent was to minus up so that we may be getting okay now in the same bar so far could be your mind exodus. You buy this stuff in the second part using first you guess we have to do? Yes. Good point of maximum. Okay. Before first of your best using could get word is minus half. Okay, so if you're anywhere, you your then minus after six. You okay? So the really getting here? This is in Chile there. What function will be essentially big busy. Okay. And if you take anywhere you smaller than minus half lesson minus minus one. So there really will be Actually, pottery and glass will be increasing and then decreasing about This will be in prison and to death because Adam it's acceptable. So minus half way, having upward off Massimo. So using position to destiny contend that maximum and excessive su minus stuff. Okay, way off. Minus half of you figure believe it. So really getting that really useless Minus absolutely be. I just want my four miss minus. Plus, you don't less than I do Musto. So where you getting is essentially when I do my best, but also on four legs, like wait for okay. In the Tardis, we have available the absolute maximum. Me. Okay, so you got a few Mexican menu. Now we have to consider the points. A few extra might call it. Because of this, we have to cover for the point which are part of the government to the in front of the door mean as they left all the point of maximum medium. Okay, so the point TVB having years and started under the men that is minus pole f off because x x UMA or bacteria living and pickles. Cool. Okay, if you find this points to the values we are going to various F minus four. Release in T minus 16 was six. So minus tan F minus. Happy learning living. Nine before and four for the beginning. Ist minus between by this 16. Yes, minus 16. Minus four minus for people's to my ethnicity. Same in this given domain. This given doing FX be having absolute maximum absolute mixing up. Yeah, execution minus half. And that this I am grateful. Okay, minimum and excessive use. So this is absolute Minya and acceptable Sue for the very, very beginning. Yes, Miss.


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