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Problem 1_ Take a look at the graph of the derivative, f' (x)_ shown below: Assume the graph extends beyond the points indicated on the graph:2f"x)-0.50.5...

Question

Problem 1_ Take a look at the graph of the derivative, f' (x)_ shown below: Assume the graph extends beyond the points indicated on the graph:2f"x)-0.50.5(a) Draw an approximate graph of the function f (x) based on the graph shown above. Attach a picture of your graph to your post: Give a brief explanation how you were able to come up with the graph:(b) Analyze the above graph of f' (x) , then find ALL inflection points, if any; and intervals where the function f (x) (not the deri

Problem 1_ Take a look at the graph of the derivative, f' (x)_ shown below: Assume the graph extends beyond the points indicated on the graph: 2 f"x) -0.5 0.5 (a) Draw an approximate graph of the function f (x) based on the graph shown above. Attach a picture of your graph to your post: Give a brief explanation how you were able to come up with the graph: (b) Analyze the above graph of f' (x) , then find ALL inflection points, if any; and intervals where the function f (x) (not the derivativel) is concave Up, and where it is concave down_



Answers

Use the graph of $y=f(x)$ to identify (A) Intervals on which the graph of $f$ is concave upward (B) Intervals on which the graph of $f$ is concave downward (C) Intervals on which $f^{\prime \prime}(x)<0$ (D) Intervals on which $f^{\prime \prime}(x)>0$ (E) Intervals on which $f^{\prime}(x)$ is increasing (F) Intervals on which $f^{\prime}(x)$ is decreasing (G) The $x$ coordinates of inflection points (H) The $x$ coordinates of local extrema for $f^{\prime}(x)$

Okay And discussion that graph is given. Okay, that is like this. I'm writing down here. This is why access this is access and the graph is like this. Okay, well at this point is three. This is the origin zero. Okay. And we have to find out. Okay, we were the graph of this function F is concave apart and where it is concave downward. Okay. And we have to find out inflection point if any. So this is the X axis and this is the texas. Okay, so we have to find out concho upward. Okay. And can kill downward. Yeah, an inflection point if any. Okay, so then the graph open upward. Okay then it will be concave upward. Okay, so when we see That from the zero. Okay. That is I'm writing down here from the zero. Okay. And when we go to the positive X axis. Okay. We can see the graph is opening upward. Okay, so from zero and it is going to in finite. So we can say it will concave upward from zero to in finite. Okay, and when we are, the graph opens downward. Okay, so here uh it is opening downward. Okay. And this point it starts from minus infinity. Okay, here it is positive infinity. So we can say it will conquer downward from Okay. From minus infinitive and it will end up to zero. Okay to zero. So and what is the inflection point? Inflection point is the point where the connectivity changes. Okay. And we can see at X equals to zero. Okay. The graph before exit close to zero. The graph was concave downward and after X equals to zero, it will concave upwards. Inflection point will be the origin. That is zero comma zero. Okay, so this will be the final answer of this question I'm writing down here. That is concave upward. Go on. Kill upward. Yeah, Mm From zero to in finite. Okay. And corn kale, mm hmm downward. Uh huh. Mhm. It is from minus in finite. 20 An inflection point. Okay. We're the conductivity changes. That is the origin point. That is zero, comma zero. And this will be the final answer of discussion. Thank you.

Again, discussion graph is given, that is like this, okay, this is X axis, this is y axis. And the graph is like this. Okay, that is this point. It is one. Okay, and this point it is to Okay. The point, this is one at this point. It is to Okay and what we have to find out where the function okay, concave upward where it is going to jail downward. And what is the inflection point? Okay, so we can see what is going give up work. Okay, first of all, john cale a blurred. So where the graph opened up. Okay, open upward. It is concave upward. Okay. And concho downward and inflection point. Okay, Inflection point. So when we see when the graph open upward. Okay, so this is the portion, Okay, this is the portion where this graph open upward. Okay. And it starts from this point that is in the mid point of one and two, that is 1.5. Okay, you understand my point At after one point x supposed to 1.5 it is going to upward and it will continue to in finite. Okay, so it will come give upward. So the interval will be 12 It will be 1.52 in finite understand. And when it is concave downward content downward, that graph opens downward. That is the whole reason that is here. Okay. And it will start from the minus infinity. Okay, it will be ro minus infinity to to this point, that is the inflection point or we can say we have we can make a tangent here. Okay at this point so it will be minus infinity to 1.5. Okay. And we ought to find out the inflection point. So what is inflection point where the con cavity changes? Okay, so we can say from minus infinity to 1.5 it is downward and from 1.5 point affinity there is okay it is upward so here One x equals to 1.5 there uh connectivity changes. Okay so y axes also given here. Okay that is that is respect to this. Okay, this is the 0.3, this is the point to and this is the 0.0.1. So at this point why will be 2.5 inflection point? It will be 1.5 comma 2.5 S. Party graph given in the caution. Okay you should refer the clear graph that is given in the question but I'll try to make everything simple. Thank you.

Okay and this question of graph is given that is like this. Okay this is why access this is X axis. Okay this is why and the graph is like this and this okay you can see this and this is the 0.0, this is one, this is one and the height, it is one by two. Okay, this graph is given in the question and what we have to do, we have to find in travel where the graph of the function F. Is conquering a port conquering downward. And also we have to find out the infraction point of this graph of this function if there is any. Okay so now no problem can kill okay concave upward and john cale downward. Yeah an inflection point. Okay inflection point. Okay we have to find out these three things. So what is concave upward and downward? If the graph open downward then it will be concave downward and if the graph opens up it will be concave upward. Okay so you can see it is the interval. Okay you I'm writing down with the different color then you can see it. Okay? It is from you can see from the minus and finite and it will be goes up to in finite. Okay. And we can see from minus and finite. 20. It is only upward. Also, it is can giving downward because it opened down. Okay and from zero to infinity it also opens down. Downside so it will always concave downward. Okay, so okay, we can say there will be no interval okay, where it is going to give up words and when it is gone care downward, that is from minus infinity to zero. Okay. and 02 infinity, understand my point. And what is the inflection point? So please don't confuse with this origin point. Inflection point is the point where concrete con cavity changes. Okay, but from minus infinity to zero and 02 infinity con cavity only downwards. So here con cavity is not changing so we can say none will be the inflection point. Okay. And these three the final answer Okay, connectivity upward. There is no point, is there concave downward? That is this point, this region and inflection point. There will be none. And this will be the final answer of discussion. Thank you.

Okay. And discussion graph is given. That is in the question, I am doing the graph here. You can also refer the book. Okay. So you can see the graph is like this. Okay, this and yeah, it is like this. Okay. And at this point this is like the graph here. Okay, so this is the point that is X equals to four. This is the point X equals two minus four. Okay. And this is X axis. And this is why access and what we have to find out. We able to find out where we're able to find out that the interval where the graph of this function concave upward. Concave downward. An inflection point. Okay, So no problem 1st of all can kill upward. Okay, and john cale downward. Yeah. Mhm. An inflection point. Okay, mm. Mhm. Inflection point. So you can see in the graph their days here when the concave apart where the graph open up. Okay, so from this region that is minus in finite to minus four, the graph is opened up. Okay. And from X equals to 42 X equals two in finite It is also opening up. So we can say open up word, it will be minus infinity two minus forward. And uh 42 in finance. So this will open up and it will be concave upward. And now for concave downward where the graph open downside, it will be concave downward. So the reason that is from minus four to plus four, this is opening downwards. Okay, so the region will be minus 4 to 4. Okay, and now inflection point. So inflection point is the point where the con cavity changes. Okay, so you can see at this point minus four before this, the grav was aboard. Okay. And after this the graph was downward. But there is a definition of inflection point that the graph graph of the function must be continuous. Okay. And where the danger line exists, But here the graph is not continuous. Okay? Or we can see, Well we can see at X equals 2 -4 and attacks equals to four. The graph is not exist. Okay. So we can see there will be no inflection point, none will be the answer for the party or we can say inflection point. So this will be the final answer. It is going to give up word concave downward and no inflection point for this graph. Thank you.


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