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3 V the Let g(2) First end V 8 1 + 67 with 8 determine e ocetion9 the polnts. any uado H axtrbich Make the 1 graph 8 8 give both increasing, thePaid Let teerei 2 th...

Question

3 V the Let g(2) First end V 8 1 + 67 with 8 determine e ocetion9 the polnts. any uado H axtrbich Make the 1 graph 8 8 give both increasing, thePaid Let teerei 2 the minium waluesd ucC IAXimu valucs 2the interval 3 Be surc indicate the prderen1

3 V the Let g(2) First end V 8 1 + 67 with 8 determine e ocetion9 the polnts. any uado H axtrbich Make the 1 graph 8 8 give both increasing, the Paid Let teerei 2 the minium waluesd ucC IAXimu valucs 2 the interval 3 Be surc indicate the prderen 1



Answers

$1-8$ Produce graphs of $f$ that reveal all the important aspects of the curve. In particular, you should use graphs of $f^{\prime \prime}$ and $f^{\prime \prime}$ to estimate the intervals of increase and decrease, extreme values, intervals of concavity, and inflection points.
$$f(x)=\frac{x}{x^{3}+x^{2}+1}$$

So this is the group off white calls extra the six minus speaking x to the 50 plus 75 extra 49 125 extra cube minus X. This is on the red crab Do you body or the first everybody in the blower up? That is why icicles toe by Frank also six x to the people I know 75 extra four plus 300 x to the cube minus stranded 75 X squared minus one. The green grab pretend now double prime or secondary body off the function that this equals toe 300 or we have a boyfriend was 3. 30 x to the fourth, minus 200 x to the cube. This 900 expert minus 75 X Now we see that the zeroes off those functions touch on the exact see So you have the zeros function off a zeros zero m five point turkey, three estimated or 3 to 8. Then the first did it. But zeros X equals toe 2.5 estimated and for 4.95 5.5. Secondly, relative zeros Ex called 1.382 3.618 and the fight you can see the blue gra period of low growth here has negative function. Um, negative from here from less than zero values who we have range off intervals. The April frame. It's less than thorough, so it's from the interval. Negative. Infinity 2.5 union this one 4.95 by 0.5 So this is the decreasing function, and we can see that F frame is greater than zero or Bob Bob Bob. Exactly. So we have the in terrible 2.54 point 95 and pipe won't survive impunity. This is an increasing function, as you could see under grab. And then you have no my minimum values. From 2.5. We get the function as the domains ranges. Negative. 2.246 point six. She's the local minimum value. Yeah, it didn't help after five months of five here and then we have approximately zero point I three, so that is another one. Minimum values low. Maximum values from Tom in 4.95 a negative 4.965 That's Laurel Maximum. This one. So from the corn came and come came downward upward for them de reparative. Second, everybody is less than zero Mhm. We have a home. Give up work from 1.38. Union one point or gets 3.62 union three points 16. 25 That is going keep downward on the intervals when this function is less than zero or below exercises. So they they scraped their dance, you know are upward on X artists that ISS called gave up work. This is from down in terrible negative impunity zero and then this one from one point or to eat toe 3.60 to this one and then 3.62 or 100 trio Tito and then pipe toe, um six and then community between five and 21. It is going live outward you see on this one. Okay, so the inflection points you have 00 asked function off or the zero that second little petite set us on the domain of the function. So we have 00 Yeah. 10. 1 point 38 and then went on Negative one on 26 1 38 Just looks one 3.62 negative one. And then when they consisted of with this one and also five negative by point, this one this that and those are the inflection points approximately.

We have given a perfect that is ableto six time X minus Expert from range. Negative five is less than or equal to X and less than equal to three. So here is the graph off. Why called six Sign X Miles Expert from negative. I'm toe positive. Three. It's the remote, even grab the blue and it's secondary crap. And we have the zeros off first, uh, function until 22.231 and zero zeroes off first three, but it ranged from negative 5 to 3 Have negative 2.98 negative. 64 negative, 2.663 and also 1.17. We have the zeroes off the second derivative range from negative to positive. Three. These are negative. 2.802 and negative 0.32 poor. Now we have to test its about the, uh, function increasing the gracing. You can see this one from from interval negative five toe negative to Protestants three or we have negative five with less than accord to X is less than two negative 2.663 This is a increasing function. It is above x axis. Then you have from negative 2.663 and negative 2.938 It is the grazing function. It is valued the acceptance off the derivative function. So we have also from negative too point my great toe. One point abilities has f prime is less better than zero. So it is increasing function and we have 1.17 toe positive three. So we have the decrease in part because it's do I promise less than zero over with well on X axis we have said the Hong Kong cavity so from negative five toe negative 2.8 to the range at the interval domain. So it is from that's from the below. Exactly. So it is a con. Keep down the world Negative 2.80 to 2 negative 34 It is open Can't came upward Because if double primaries above X axis and then we have from the range negative three pointer to port two or three So it is below IRC So is open up. I'm down the world on cavity so we have also the inflection point We said the inflection points here the zero off off the secondary positive to have this one. So we have complex shown points. So we have. First, we have negative two points to point it. Zero It two point negative. 2.802 So it's points, I think the 2.8 and negative 9.8 people approximately. And then you have negative 0.34. Um, point negative. Productive point again. 2.11. That is the inflection point. So you're the family off this answer. So we have been terror balls or we have in their backpack negative three functions. Um zero inter battle the Hong cavity and inflection points.

I'll give them where her back falls expert minus one. But I wanted to For Tex killed less X plus one first. Everybody on online stores have this one portion troll. Then we have experiments wanted wanted to for excuse express one minus. Yeah, they live. A people are excused experts one on the experiments one number or express express one squared to have this one. The experiments one is to x the derivative forex. Cuba's experts one because you know, between the experts one. So we have here of two x the quantity for X Cuba's express one minus quantity on 20 experts. One So quantity expert Mention about the quantity or excuse experts ones. But so we have equal to negative What the export was 180 one x squared. Pressed to express one hour for X or the X Cuba's express once word second the room. But he also opened the hoster and this one in the result will become 80 extent. The quantity for the experiment 243 X Q. Minus seven. Expert ministry expressed over the quantity for the X Cuba's express one to the killed. When this tropical calculators off, we have the function. The red grab, the blue grew up. It's the the first everybody and the green group is the secondary beteen a So you can see we have the asking talkto the grab that is X because negative 0.264 That's the approximation. So we have first zeroes off the function the first three but the ISS ex cons negative 1.77 point 75 When the function zero is executes negative point and one the secondary tables Excellence Negative 2.54 time negative 0.2230 and 2.48 to attack group. You can see that those zeros zeroes off first of beauty, they know you have to secondary Beti, Our first everybody in the secondary body now we have to do now is the intervals. We can see that on the intervals there is decreasing function. If prime miss less than zero can see under grab, we have now the decreasing functional negative infinity and negative one 0.733 This negative then Well pastie crazy value punctuation from negative 1%. 70 Need active top negative 0.264 Then you have also Yeah, problem Negative. They also increasing function from negative two points 641 from 7 to 5 Increasing past function if one is greater done. A prime creator than zero This one this Chris Intervals to policing function from Miss Quested zero So 1.75 infinity. So these are the intervals increasing increasing function. And then we have contact pity in terrible and down the words The interval of top bubble prime is less than zero and the upward if double prime is later than zero. Just start up both so called derivative And then we have interval negative infinity and negative 2.45 to pass it the home keep aboard and also have the negative. I'm have 2.482 and in the days Yep. Somebody we have that word. So negative to six party role. She's going to see the pipe portent and upward Negative in 20 negative Perfect for negative Took more points Negative 06400 point to survive and to point for that infinity where the inflection points zeroes off the second the they believe in Let us the X on the functions in fact, inflection point negative. 2.454 negative through eight. Negative. 2 to 3 negative toe a pipe, zero negative one and two one for 20 0.8 We have the stable partner and those values Intention point here. Here. Yeah, are those inflection points and those are zero in their ball Concha beauty and the inflection points.

So you have the photograph of a pub exit physicals toe for export minus 30 toe excuse because 18 X squared minus 95 X plus 29. This is the regular function. It's derivative is above the prime X calls 16 x cubed minus 96 X squared plus one on a 78 x minus 95 This is the blue group and the secretary body off function of X f double prime X Statistical support expert Minus 192 experts 178 This is the Green Group. They was movement zeros, zeros of the function. So the zero function we can see on the grab of the function of X that zero or 80 point pipe and 1.60 to the first derivative zero that this 0.921 and 2.5 and the secondary body zero that it's equals toe one exposed to 1.46 2.54. This is the zeroes off function, its first derivative and the secondary body from the crops off f rhyme. We estimated that the F prime is less than zero. That means the function is decreasing from this in this interval from like the infinity and tow syrup ignited between that and union off two points don't mean 2.72 point eight. That is discreet increasing function. Because, as we can see on the graph, we have this zeros as it's in terrible. And then that from the derivative in terrible. So we have decreasing function. So we have now the increasing function from the derivative is greater than zero. Seen the crap from 0.92. This is positive value toe 2.5 and also 2.58 Infinity, that's increasing function. As you can see, this is increasing function. So the crap off, pop, right, Make it clear that function its maximum the minimum near the two point, but which is no more very in the last scrap from the group off the secondary. But we estimated that the secondary. But it is greater than zero that this f ISC on Cape Upward and that does inter bottle off. I can't give up whatever negative infinity and 1.46 also union toe 2.5 infinity. As you can see the home cape upward the home. Keep downward for 1.46 2.54 if f double my miss less than zero. As you can see on the grab, it's less than zero or below the X axis later than zero about the X axis. So in a double, prime is greater than zero concave, downward for 1.4 to 6 to 2.54. I know you can see the inflection point at 1.46 negative 1.4 and also 2.50 40 for 19. And that's what this is. The zeroes off the the secondary. But that indicates that this Dominus a implication point, as you can see on the graph, so that is for explanation for this one.


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