5

I 8 8 V 1 1 1 F F li 8 1 V lu} { 8 F } | W 1 # Ml 8 1 H | H F...

Question

I 8 8 V 1 1 1 F F li 8 1 V lu} { 8 F } | W 1 # Ml 8 1 H | H F

I 8 8 V 1 1 1 F F li 8 1 V lu} { 8 F } | W 1 # Ml 8 1 H | H F



Answers

(a) $\mathrm{F}_{1}(\mathrm{a}) \mathrm{F}_{1}^{\prime}(\mathrm{a})+\mathrm{G}_{1}(\mathrm{a}) \mathrm{G}_{1}^{\prime}(\mathrm{a})$ (b) $\mathrm{H}_{1}(\mathrm{a}) \mathrm{H}_{2}(\mathrm{a}) \mathrm{H}_{3}(\mathrm{a})$ (c) $F_{r}(a) G_{r}(a) H_{r}(a)$ (d) 0

Hi, this is Claire. So Hi, this is Claire. So in number two of Stuart's my calculus book, So we have eight parts. This problem the 1st 1 It's on the dir votive of zero. So the two points are 00 As you can see here on 14 it could be estimated, and the derivative gives us So Ciro's 14 so derivative the rise of a run gives us four for be. The horizontal tangent can be drawn at, um, excess as X equals one. So the derivative acero for seeing your ex eagles to the graph goes down half half a unit for every 1/3 of a unit to the right. So the derivative is negative, 1/2 over one that gives us negative three House Ferdie near X equals three. The graph goes down, the graph goes down a unit and it goes one to the right. So the derivative gives this negative one Near X equals four. It's similar. So it goes down one unit and to the right. So it's also negative. One for X equals five. The graph goes down 1/10 of a unit right here, and then it goes um, 2/2 unit to the right. So rise over run gives us negative 1/5 and Fergie. It's similar to be so at ethical. Six. Ah, horizontal tension can be drawn, so it's gonna be through. And for a tsh at X equal seven, their approximate points are seven and negative. 1.8 then ate the negative 1.5. So the derivative is Syria 0.3. And when you plot all of these at 00 it's gonna be for going to do this and read so four and then at 10 at two. It's negative. Um, three house, the negative one. No good of one negative. 1/5. It's gonna be around here. Zero, then 0.3. So the grass gonna look something like this? What?

So looking at this graph, we want to determine the different values. Um, given thesis slope of the graph forgiven F But we want to find f at that private certain values. So at zero, we see that this is a pretty positive slope. Um, we see that by the time it covers x distance, it's gone about 1 to 2.5. So we're going to say that this slope is 2.5 at this 10.0. Then a time of one is going to be zero, because at this point, it's leveling off and then changing direction. Then f prime of to is going to be a negative slope, and we see that it would probably be negative. One half are very negative 1.5 based on the exchange in exchange, in wine after crime of three is going to be, um, 123 At this point, it appears that we have a slope of negative one. So starting to stabilize a bit as we see not only in the derivative function but in the graph to f of four, is going to give us about a slope of maybe negative 0.75 So once again, the negativity slope of our graphics slowing down then f of five we can expect to be even, um, higher, technically, some for dealing with negatives. So at five, we have very close to zero. Um, in fact, this would probably be about, um, negative point to maybe negative 0.0.25 perhaps even like closer to zero at six. It's pretty obvious that the slope is zero because we're changing direction. And then at seven, we start to get positive slope again. And based on the graph, it appears to be a very minor, so probably something like 0.25 again.

In this problem. We asked our ass to find the center of mass of this two dimensional system with the masses. 2 8 to 1 and four in the positions. Negative three negative. 100 And negative one, too. In order to find the center of mass, we first need to calculate the center mass in the ex direction, which we will do by calculating the moment in the UAE direction divided by the total mass. Once you've done that, we will calculate the, um, center of mass in the wind direction. Just calculate the moment in the ex direction of over the center of mess. Okay, So calculating Expert, um, the moment of wise calculating by multiplying the masses by the X coordinates. So we have eight times negative. Three plus one time, zero plus four times negative. One all over. The total mass, which is given by eight plus one is nine plus four gives us 13 doing some arithmetic. We can find out that eight times negative three is negative. 24 0 minus forgives us negative. 28 over 13. Now, to find the center of mass in the UAE direction, we're going to take the moment of X, which is the masses times there. Why Coordinates? So we're going to have eight times negative. One plus one time, zero plus four times two all over the total mass, which is still 13 here. Only two are particularly. Get negative 80 plus h, which gives us zero over 13 for our center of mass. Explore why BAR is given by the coordinate point. Negative 28 over 13 from a zero.

Okay, so we have wise equal to you. Cute and using eight X minus one. So you can differentiate Why? With respect to you and that's just six. You squared and then we can differentiate be with respect, Excuse function of X, get AIDS. And so what the general says is if we want the derivative of why would respect eggs This is D y t yu times to you the x which is six. You squared times eight, which is forty eight you squared. But we want our final answer to be in terms of X so we can just substitute in, but you is is a function of X. So this is forty eight times eight x This one, It's weird.


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