in-each-part-sketch-the-graph-of-a-continuous-function-f-with-the-stated-properties-a-f-is-concave-u

Question

In each part, sketch the graph of a continuous function $f$ with the stated properties.
(a) $f$ is concave up on the interval $(-\infty,+\infty)$ and has exactly one relative extremum.
(b) $f$ is concave up on the interval $(-\infty,+\infty)$ and has no relative extrema.
(c) The function $f$ has exactly two relative extrema on the interval $(-\infty,+\infty),$ and $f(x) \rightarrow+\infty$ as $x \rightarrow+\infty$
(d) The function $f$ has exactly two relative extrema on the interval $(-\infty,+\infty),$ and $f(x) \rightarrow-\infty$ as $x \rightarrow+\infty$

Carson Merrill · Accepted Answer

So for this first function, we see that there is one relative extremely and, um, the entire graphics con cave up we see for the second one. Um, there is no relative extreme a but it is calm. Keep up across the entire interval for this graph. Here we see that there are two relative extreme are here and here. And as X approaches infinity f of x purchase infinity Then lastly, we see that there are two relevant relative extreme A here in here and as X approaches infinity f of x approaches native city.

Carson Merrill · Answer

so his problem. The first thing we want to do is have a graph with one rail too extreme, Um, and have as FX approaches zero X to go to infinity and extra go to negative infinity. So, um, what that&#x27;s gonna look like is I will say as ex ex FX approaching zero as X goes to infinity. So look something like this. And then it&#x27;s also going to as experts negative, unique. But we also want a relative extreme in there. So what? Weaken Dio is at this little hump in there and continue it? So now we see that we have one relative extreme A and F of X approaching zero as X goes deposit infinity and negative insanity.

Carson Merrill · Answer

This is a graph that is increasing. Um, on the interval from negative infinity deposited infinity. Um, and what that tells us is that the f prime will be greater than zero, and f double prime will be less than zero. Um, we can also have a graph such as, um, one that, uh is decreasing here. We could do something like a negative x squared. So that should be one. That is, um, con keep down. But it&#x27;s ah in order for it to be decreasing, we want something more, um, along the lines of a well do negative e the acts. But something like this. Ah, Although we wanted to be foot to so for you, this then it&#x27;s, um it&#x27;s increasing on this interval on it&#x27;s also con cave down. What that tells us is that F prime is greater than zero. But f double prime would be less than there. And then we want Khan gave up and decreasing. That would be, uh, this would be if we dio conch it up and decreasing this week on cave up in decreasing here. Essence, it&#x27;s decreasing. F prime would be less than zero, but f double crime so this conclave up would be greater than zero. And then, lastly, we won&#x27;t con Kate down in decreasing. That would be something like this. That would be f prime is less than zero enough. Double prime is less than zero as well.

Carson Merrill · Answer

So for this graph, we&#x27;ll do X Cube. This one is increasing the whole time. It has an inflection point of origin, and it&#x27;s con cave up from zero to infinity. I&#x27;m here. The f prime would be, uh, f prime would be great. And zero as a double crime would be less than zero. Uh, when x is less than zero and it would be greater than zero when x is greater than zero. Um, then we could do something for this next problem. Like, uh, say the cubed root of X as Sophia the Queudrue of acts here, This would be, um, con cave down from zero to infinity, but still increasing with the inflection point at the origin. This would still be f prime greater than zero. But in this case, the F double prime would be less than zero. Um, would be greater than zero. But when exes lesson doing and it would be less than their when X is greater than zero, uh, then we wanted decreasing. Um, a decreasing function here would look like, um, if we dio okay, um X a negative x cubed. I&#x27;m right here. That should be decreasing. Um, and we want to be Kong cave up from zero to. So what we&#x27;ll do here at fix that will do something like this. And like this. This way it&#x27;s decreasing, but it&#x27;s Kong cape up from zero to infinity. Um, with this F prime would be less than zero. Uh, f double crime would be less than zero in the first section from Negative Infinity zero. But then it would become greater than zero a to this point. Um And then lastly, we wanted decreasing with an inflection point at the origin I&#x27;m in conclave down, such for this one will come in handy. It&#x27;ll be con cave down from zero to infinity and decreasing. Um, that tells us that f prime zero Well, a little bit less than zero and then f double prime will be greater than zero. Um, from negative. Infinity zero. With an zero to infinity, Abdullah prime will be less than zero

Fahad Paryani · Answer

Okay, so we&#x27;re given I draw the graph of F crime fellow and were being asked about the different things that the function So for a were asked about what already interval and increasing or decreasing. So for this we simply look at whether the function is positive s O that occurs when the function is above the graph. Because remember, this is a crime. And this occurs from zero two two and from forty six. And then this is actually eight right here that this is a sorry about that. And this is from eight to infinity. So this is increasing and then it is decreasing everywhere else. So that would be from two, two, four and sixty eight. So it is decreasing here. Ah, for local max in man, we have local backs and men&#x27;s. Okay, So local max occurs when it goes from positive to negative. So this occurs from process negatives of Mexico&#x27;s too so local Mac two. And then it occurs again at night at six. Because it&#x27;s going from positive to negative at six, two and six and then local men occurred when it goes from negative to positive. So this is from negative to positive. So that&#x27;s four and negative to positive again at eight. So this is it for sea on one two intervals is a conclave. Absolute. So it is. Khan gave up when the ah slope s So when the functions increases with the equation So cardio occurred. Ah, from the sea when the slope is increasing. So this is you could see this is decreasing and then it&#x27;s increasing from three to six. It is increasing. This can&#x27;t give up and then it again increasing from six to infinity. And then it is Kana Cave down when the slope is negative, so decreasing This is from zero three and that is it. And then for d were asked Ah, there any inflection point? So there&#x27;s an infection point of Mexico&#x27;s three because the sign changes, It goes from a negative slope to a positive floats. And so that means the second derivative is changing and by definition, infection, pork ribs. When the Khan Cabinet changes or the sign of the second derivative changes, that&#x27;s X equals three and then for e. We&#x27;re going, Teo Graff said this is a prime for being asked Graff Ah, the graph of f and we&#x27;Ll do it on the next page and we&#x27;re assuming that half of zero zero So we&#x27;LL start right here. And basically it increases and decrease is giving us a local men right here. And then it goes off to some Ah, remember, has a whole goes off so positive and it goes up to a very high point wherever this point, maybe s O goes after that point and make This is not exactly the skill it comes down. There&#x27;s another local big the increasing. So it&#x27;s not exactly the best graft, but this is a right here. These are like critical point. This is sick and this is a vertical ascent. Oh, I mean, not every glass it Oh, sorry. Just a I&#x27;m just drawing this to show you that there is a, uh it&#x27;s sharp corner here is continuous because I&#x27;m so sorry. This is continuous because it&#x27;s told us. But the graph of a continuous function f so this is still continue to just have the sharp corner that&#x27;s quite a derivative doesn&#x27;t clear. And then this point right here is for because again, this is a local backs and bitter this another local. This is a local better. This is a local back, though that we have identified him early admissions Go

Fahad Paryani · Answer

Okay, so this is a graph of prime right here, and we&#x27;re being asked about different things about the function F so it&#x27;s just go ahead and jump right into it. So we&#x27;re being asked where efforts increasing, decreasing. So we just simply look at where the function is above the exactly for positive. So that is increasing for that occurs from Ah one, two, six the one, the sixth and eight to infinity. And then it is decreasing where it is below the X axis. So that&#x27;s from zero to one and then from sixty. Oh, that looks like an infinity, Uh and then for be where they asked the local maxim men So local back and local big So America our local backed occurs when it goes from positive to negative and then from right and the local medical from negative to positive. So this is going around negative to positive. So that&#x27;s a local red at one and occurs at it again. And then a local Mexico&#x27;s at six. Because going from positive to negative and that con cave up occurred when the slope is positive or increasing. So that&#x27;s occurs from zero to two and three to five and for seven to infinity and then call it a cave down occurs when the slope is negative and this occurred between two and three and five and seven. The inflection point occurs when the slope changes and the slope changes only when there is a some sort of local back from manicuring so gently where the tenderloin is zero. So if you look at the point where potential injury you have two, three, five, and seven So those are inflection point practical two, three five, seven to draw thgraf Of f What we do is we had just drops of access Maxie&#x27;s So we are told that it is decreasing from zero one and then we have a local men at one and that it is kind of gave up from zero to two. So it&#x27;s gonna look something like a U. But going down, what&#x27;s going on? You have a local band right here want this will be one and then I believe that it increases from one to six is increasing and then it room it. Ah, it is Khan cave down for between no, from zero to still can&#x27;t give up and then it switches that too, So it would look something like good. We&#x27;Ll continue to rise and that will stop it. Three. Cliff they don&#x27;t go up because ah, see between So we&#x27;re still at the way we go. Two sixes increases over all the way to six. It was increasing all the way to six that we have local Max. It&#x27;s six, remember? Ah, little back. That&#x27;s six. So that&#x27;s why I stopped right there and that it goes down from there From six to eight, Stuff of sixty eight is decreasing and there&#x27;s a local mid at eight. So we&#x27;re going to go all the way down and it&#x27;s gonna and it comes down to be some kind of local bed and then I think it goes. Officer increases from eight to infinity. So this has to go all the way. I like it. This will be six one. This is a This is a rough sketch of half through all of the information given to us

Problem

In each part, sketch the graph of a continuous fu…

Problem 1 Easy Difficulty

Answer

graph

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Howard Anton, Irl Bivens, Stephen Davis

Calculus Early Transcendentals

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Calculus Early Transcendentals

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Precalculus Review - Intro

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Howard Anton, Irl Bivens, Stephen DavisCalculus Early Transcendentals

Grace H.

Caleb E.

Kristen K.

Samuel H.

Howard Anton, Irl Bivens, Stephen Davis

Calculus Early Transcendentals