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2.6 Score: 3/10 3/8 answered8 Yo _Question 8C0r2 pts ' 10099DetailsConsider the function f(z) rlelrf(x) has two inflection points at X = C and X = D with C <...

Question

2.6 Score: 3/10 3/8 answered8 Yo _Question 8C0r2 pts ' 10099DetailsConsider the function f(z) rlelrf(x) has two inflection points at X = C and X = D with C < D where C isand D isFinally for each of the following intervals, tell whether f(z) is concave up (type in CU) or concave down (type in CD). (- 0,CJ:[C,DJ:[D, 0)Submit Question

2.6 Score: 3/10 3/8 answered 8 Yo _ Question 8 C0r2 pts ' 100 99 Details Consider the function f(z) rlelr f(x) has two inflection points at X = C and X = D with C < D where C is and D is Finally for each of the following intervals, tell whether f(z) is concave up (type in CU) or concave down (type in CD). (- 0,CJ: [C,DJ: [D, 0) Submit Question



Answers

$31-32$ The graph of the derivative $f^{\prime}$ of a continuous function $f$ is shown.
(a) On what intervals is $f$ increasing? Decreasing?
(b) At what values of $x$ does $f$ have a local maximum? Local minimum?
(c) On what intervals is $f$ concave upward? Concave downward?
(d) State the $x$ -coordinate(s) of the point(s) of inflection.
(e) Assuming that $f(0)=0$ , sketch a graph of $f .$

Were given the graph of the derivative F prime of a continuous function f This is found in exercise 32 of this section part a has to find the intervals on which the graph well, in which the function F is increasing or decreasing. Well, we know that F is increasing when f prime is positive and this is on the interval According to paragraph 16 and eight Infinity likewise you have that f is decreasing where f prime is negative. According to our graph, this is on the interval negative or 01 and 68 In part B there has to find the values of X at which f has a local maximum or local minimum Well, we have the f has local maximum where f prime changes from positive to negative and we see looking at our graph this is the point X equals six. Likewise, f has the local minimum where f prime changes from negative to positive. Looking at a graph, we see that this happens at X equals one and X equals eight part C, whereas to determine the intervals on which f is con cave upward or con cave downward Well we have that f is con cave upward where f prime is increasing and looking at the graph of f prime, we see that this is on 02 on the interval 35 and on the interval seven. Infinity. Likewise, we have the F's con cave down where f prime is decreasing, which, according to our graph, is on the intervals 23 and 57 in Part B were asked to find the X coordinates of the points of inflection. Well, we know if their points of inflection where f changes direction of can cavity, could you just say F changes can cavity? And according to Part C, this happens at X equals two X equals five and at X equals seven and finally in part E were asked to sketch a graph of F given that f of zero equals zero. So I'll graph 1st and 4th quadrants only. Mostly the first quadrant X and Y axes. You know that there's a point at the origin 00 Now we know that the domain of this function is going to be from zero to infinity since this is the domain of the derivative. So we're working with and we have that f is decreasing on 01 For starters, we also have that f is con cave upward on 01 So we have half of the bowl like this and I guess she really label all these exes first. So X equals one, 23 or five, six, seven and eight. Now, we also know that f is still con cave upward on 12 and f is increasing on 12 So we could say go back to the X axis. X equals two. Now, once we're here, we have that FS still increasing on to up to three. And we have that f is con cave downward on 23 So we're going to switch con cavity. So I make this a little bit steeper here and then switch common cavity still increasing till I reached three. Now, once we reach three, we have the f is still increasing from three 25 And we have that if his con cave upward now from 3 to 5 surging again, switch can cavity. But without the horizontal lassitude. So scale this a little bit differently. There we go point like that, and then you see the F is increasing from 5 to 6. In fact, it has a local maximum at X equals six and we have it. F is con cave downward from 5 to 6. So we're gonna switch can cavity and re increasing. So I said this is a local maximum certainty decreasing on the interval from 6 to 7 and also pancake downward on the interval from 6 to 7. Do you maintain the same kind cavity? Now here we have that f is still decreasing from 7 to 8. But we see that f changes can cavity to con cave upward from 78. So we changed in cavity again and then we have that at eight x switches. So that becomes increasing on eight to infinity and is going to be con cave upward made to infinity Same confab ity. So we get something like this the rest of the function and so we have constructed graph which matches the conditions impulse

Yeah. So for the m problem we want to find on what intervals is increasing or decreasing. So let's say we have some random function. Well look something like this, we c we can take its derivative and when we take its derivative, I'll find that there's these points Where the function equals zero and those are going to be these points right here. So they'll end up giving us the value along the X axis. So I'll tell us our function is increasing when the slope is positive, meaning that are derivative, graph is up here, so that's going to be portioned like this um portions like a portion like this as well and the functions be decreasing and those other portions right here and right here then we see the graph is going to be concave up in concave down in different areas that we can keep down right here and concave up right here and then concave right here and concave down right here. That's going to be our final answer.

Yeah. So for the m problem we want to find on what intervals is increasing or decreasing. So let's say we have some random function. Well look something like this, we c we can take its derivative and when we take its derivative, I'll find that there's these points Where the function equals zero and those are going to be these points right here. So they'll end up giving us the value along the X axis. So I'll tell us our function is increasing when the slope is positive, meaning that are derivative, graph is up here, so that's going to be portioned like this um portions like a portion like this as well and the functions be decreasing and those other portions right here and right here then we see the graph is going to be concave up in concave down in different areas that we can keep down right here and concave up right here and then concave right here and concave down right here. That's going to be our final answer.

He is. Claire's a one namer here. So for her forgiven our function, we're going to differentiate it. Yeah, for men, it's cute. Over its waas it was 27 for a function to be increasing, the problem has to be bigger than surround. So we plugged in and you get access to figure that out. Then it's increase one in purple, through koala affinity for reflection to be decreasing. But the problem is small islands are you when we plug it in and get that's a slope in Syria. So we know that stick Grace Morton. But Interval Make it of infinity. Coma for party. Griffin on differentiated again to find her second derivative ex Claire Time Thanks to you before twenties, anyone over. Thanks to the form because 27 squared to get local men or Max, you have to say our prime to be syrup in software connects. So step execute, order. Extra work. Pickle serum. Yeah. Texas equal to Sarah. We're gonna put this thing to weaken derivative. We get zero. So this lotion has neither local men more local max court scene. We're gonna use our contractor test. So of double prime quicker than zero it's called Kapok. This occurs when next swollen, committed. Three. Oh, so 23 smart Interpol is negative. Infinity Negative. Three through three. For it to be calm. Keep down. It's just a whole person. This occurs when access bigger than three. What? Negative Three So comfortable here. And our opponents of inflection, Sarah and positive Negative. Great party. We're going to draw stopper Guard. That seems Well. Try eating right. No, look, something like this.


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