5

Score:11.4.23For Kx) = Iind an quallon for tho 50canti Lno Inrough the polnts whoro % = and K26.For IxJ = find nn equation Ior the Iine tangont lo the curve when x ...

Question

Score:11.4.23For Kx) = Iind an quallon for tho 50canti Lno Inrough the polnts whoro % = and K26.For IxJ = find nn equation Ior the Iine tangont lo the curve when x =4The equabon for Inu secant k ne isy =Enlet your anowor Ino dnawiol baz wnd Inor cliok Chock Anawon Ranalningesc

Score: 11.4.23 For Kx) = Iind an quallon for tho 50canti Lno Inrough the polnts whoro % = and K26. For IxJ = find nn equation Ior the Iine tangont lo the curve when x =4 The equabon for Inu secant k ne isy = Enlet your anowor Ino dnawiol baz wnd Inor cliok Chock Anawon Ranalning esc



Answers

Let $ g(x) = e^{\alpha} + f(x) $ and $ h(x) = e^{kx}, $ where $ f(0) = 3, f'(0) = 5, $ and $ f" (0) = -2. $
(a) Find $ g'(0) $ and $ g"(0) $ in terms of $ c $.
b) In terms of $ k, $ find an equation of the tangent line to the graph of $ h $ at the point where $ x = 0. $

This Parliament here on this problem. We have a polynomial that we would like to grab. And since we want to use a graphing calculator on, I'm just gonna use Dismas here in order to draft Now we are graphing X to the 4th. It's the form mine is to execute plus 10 X minus 26. So here on Desmond's we can just type it in just like this. Okay. And that'll give us this craft. Yeah. And what's something kind of like that? No, says it goes up and up forever and ever as you go to the left and the right. Now we also want to find where f. of X is greater than -1. And so let's graph Y equals -1. Yes. So for graph Y equals negative one and gives us that line there. We care where it intersects with the other one. And let's find that point there. So the first point where they intersect that is negative 2.236. And so what that means is that if X was smaller than negative 2.236. Okay. Effect was less than that noticed that are blue part or blue graph there is above. So it means our first part is whenever X is less than negative 2.236. That's another point over here is positive 2.236. And so that means that effect is larger than 2.236. Then that means our polynomial is above. That's fine, negative one. So those are so anytime it's plus the negative 2.236 Or any time that's bigger than positive 2.236.

This Parliament here on this problem. We have a polynomial that we would like to grab. And since we want to use a graphing calculator on, I'm just gonna use Dismas here in order to draft Now we are graphing X to the 4th. It's the form mine is to execute plus 10 X minus 26. So here on Desmond's we can just type it in just like this. Okay. And that'll give us this craft. Yeah. And what's something kind of like that? No, says it goes up and up forever and ever as you go to the left and the right. Now we also want to find where f. of X is greater than -1. And so let's graph Y equals -1. Yes. So for graph Y equals negative one and gives us that line there. We care where it intersects with the other one. And let's find that point there. So the first point where they intersect that is negative 2.236. And so what that means is that if X was smaller than negative 2.236. Okay. Effect was less than that noticed that are blue part or blue graph there is above. So it means our first part is whenever X is less than negative 2.236. That's another point over here is positive 2.236. And so that means that effect is larger than 2.236. Then that means our polynomial is above. That's fine, negative one. So those are so anytime it's plus the negative 2.236 Or any time that's bigger than positive 2.236.

We have to compute re months. Um, by the function effort, X is equal to ex spare less eggs and the partition p for the function in east zero comma one. I wanna 2.5 Kromah, 3.2 coma life and something Point C is equal. Do 45 going on. So three glamour 4.5. We know that the final left re months, um are you into their karma equals C is equal toe if, uh, see one, then, uh, X one? Yes. If see toe, then. Uh, that's good. That's if, uh, C three, then, uh, X three less. Therefore see, for there's got export. This is equal to if, uh, white. Why? Into one minus zero Last if, uh, toe into 2.5 minus one. Less if, uh, three in tow. 3.2 minus 2.5. Yes. If 4.5 in tow, five minus three point door. This is equal to zero point 75 in tow. One less. Six into 1.5 less. 12 into 0.7 less. 24 points. 75 in tow. One point. And if we calculate all these, we will get biggest people point. They were

For this problem we are asked to sketch the level curve, Z equals K. Where Z equals x squared plus one over X squared plus y squared and Kay equals 124 Which means that essentially we have K equals x squared plus one over X squared plus Y squared. So to avoid having to rely on my lack of artistic abilities, I'm going to jump into some plotting software to show this. Alright, so here we are. You can see the straight lines at Y equals one and Y equals negative one. Those correspond to when K equals. You know, if we have X squared plus one over X squared plus Y squared equals one. Then that would require that Y squared equals one. So why it was plus or minus one. Then we have check here. If we remove forward from the list. So we have this line which passes through X equals plus or minus one when Y equals zero. And then lastly when we have K equals four, we have another ellipse inside.


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