5

13. [0/1 Points]DETAILSPREVIOUS ANSWERS LARCALCT1 2.5.061 . Find the points at which the graph of the equation has vertical or horizontal tangent 81*2 36y2 line 972...

Question

13. [0/1 Points]DETAILSPREVIOUS ANSWERS LARCALCT1 2.5.061 . Find the points at which the graph of the equation has vertical or horizontal tangent 81*2 36y2 line 972x 648y 2916 horizontal tangents (x) 43 (smaller Y-value)(Y)6,22.3(Iatger Y value)vertical tangents(Y)(sraller x value)(larger value)

13. [0/1 Points] DETAILS PREVIOUS ANSWERS LARCALCT1 2.5.061 . Find the points at which the graph of the equation has vertical or horizontal tangent 81*2 36y2 line 972x 648y 2916 horizontal tangents (x) 43 (smaller Y-value) (Y) 6,22.3 (Iatger Y value) vertical tangents (Y) (sraller x value) (larger value)



Answers

Tangents are drawn from the point (0,3) to the parabola $y=-3 x^{2} .$ Find the coordinates of the points at which these tangents touch the curve. Illustrate your answer with a sketch.

So the reason about where a function is horizontal, we need to find where is the derivative equal to zero. Remember the derivative means the slope of the tangent line. And if a line is horizontal, its slope happens to be zero. So let's find the derivative. Which we could denote a number of ways. Maybe D Y. The X or Y. Prime. The derivative of X cubed by the power rule is three X squared. We bring the three down as a coefficient in the power is one less. And then we'll subtract well the derivative X squared, bringing down that power would be two X. And now to the first. So there is our derivative. And to be horizontal we need this to be zero. So let's solve for X. I notice X is a common factor. And since that product is zero, either X could be zero Or three, X -2 could be zero. So we already found one value of X. And by manipulating this we can get X equals two thirds but were asked at what points This occurs. So we also need the Y value that goes with these excess. If we plug in zero for X we get zero cubed minus zero squared, but that's zero. So the first point in question is 00. We plug two thirds into our function. We get two thirds cubed which is eight 27th minus two thirds squared, which is 4/9 But that's the same as 12/27. So that gives us negative four 27th. So are other point is two thirds common, negative four 27th. And these are the two points where our function is horizontal immediately at that instant. Or another way to say it is where the tangent line is horizontal.

All right, So in this problem, we have this wife whose x cubed minus three X minus two function. And then this problem has again two points in the first part. We're gonna find horizontal tensions. So we know that the horse and attendants happens when the first derivative is equal to zero. So we're gonna figure out the first derivative and set it equal to zero. So let's do that. The first derivative equals zero. So from there the first year, but it will be three X squared, minus three equals zoom. And if I sold this equation, we're going to get X squared is equal to one, and from there it's gonna yield us two answers. The first ones ex schools one. The 2nd 1 is X equals negative. So now I need to take these X equals one and X equals negative one values. I'm substance back into the original function. So why one is gonna be cool to just one cooped minus three times one minus two. So from there, it's gonna be just negative four. So basically one come up. Negative four is going to my point of tendency. Another one. Why off negative one making one cooped minus three times naked one minus two. And it's gonna yield us zero. This is another, uh, point of tendency, which is negative. Warm Come up, Z. So basic at these two points, we're gonna have to horizontal tensions. And also in the first. But it says, what are the slopes off the what are the equations off the perpendicular allies? So they questions equations of the political alliance will be X equals one and X equals negative one. Because at these two points, we're going to have a vertical tangents. Okay, so this is the first part. All right, let's move on to the second port in the second port again. We're gonna deal with the smallest possible smoke value and that this function ever has. Okay, but for that, we need to figure out what is the M over DX and wanted to set this equal to you. Okay, so the M over the X will be just six X instead of the coke zero and from their exes, got a vehicle to just zero. So now you need to take this X equals zero value and substitute back into the white prime function, which is the slope, okay? And why Prime of zero is gonna be culture. Let's remember what? His wife front. It's three times zero squared, minus three. And from there, and why prime of zero is gonna be equal to negative three. Okay. And this is a smallest possible valley, which is negative. Three. And what is the point of Tennessee where this slope happens? So if I If you want to figure out the point of agency again, you're gonna take this X equals zero and substance back into the original function. So why off? Zero is gonna be cool, too. Zero kept minus three times zero minus here and from there. Why have zero is gonna be a culture negative too. So this smallest possible smoke value is going to take place at this 0.0 comma. Negative. So that's the point off tangent C. So now, in the in the second part of this part beat. I wanted to figure out this smoke off the women's figure out the slope of the proper nickel lion and the equation of it. If my slope is negative three the slope of the perpendicular line will be and one equals 1/3 because, you know, uh, negative. Reciprocal. Okay, so it's gonna be negative. Want it's gonna be positive 1/3. So using this slope of the perpendicular line and this point of tendency, we can easily create the equation of the purpose. So it's gonna be called up. Why? Minus negative here. Pickles. 1/3 times x minus is you. And if I simplify this working again, why plus two equals 1/3 times X basically. And this is the equation off the normal. My Okay, So I'm gonna leave my answer in this point. Slow for

The underlying theme in this is if you have a horizontal tangent that basically we're saying I want to use the same notation because they're talking about why equals then d y d x at certain X values may Don't even say it x equal c I must have the equation of the derivative should equal zero somewhere. And, uh, usually there's a little space there. Sorry about that. Um, that's the overall premise of this problem. So what we need to do is personal right out the equation two x cubed. But then what I'm gonna dio okay is find the derivative of this. So do you wind the X? What, equal six? Because you bring them three in front times to a six x squared minus 54. We're going to set that equal to zero. So now what I can do is add 54 over divide by six to solve for X squared. Um, but I would simplify that because both those numbers are divisible by Ah, I think by six, right, you will get nine eso when you square root both pieces. Um, you would get plus or minus three. So the two places on the point on the curve. Uh, now, what I need to do is go back to the original problem and plug in three and negative three. And for these exes to figure out what those values are. So three Cube is 27 times two of the 54 minus 54 times three plus one, which should be 54 times to be negative. 108 plus one would be negative. 107. So that would be a point if excess positive doing this in my head, by the way. So if I'm slightly off, I'm sorry on then, Negative three. When I cubit will be negative 27 times to be a negative 54 and there will be a plus a 54 times three. So that should be a positive 108 plus one would be 109. So, assuming I did my math correctly, I think other eight points here

First things first, let's take the derivative and we end up with three y squared. Minus 27 equals two ax times. Derivative of acts over his DX over jacks, ex primes. The same thing. Okay, we know that X prime is zero. Therefore, three y squared minus 27 equals zero. Therefore, why is plus or minus three Now we know that plugging in we end up with negative 54 equals X squared minus 90 X squared is 36 x equals plus or minus six and then we have negative three squared plus 27 times three equals X squared minus 90 Solve for accented with X squared equals 144 x equals plus or minus 12. Giving us four points. Negative 12 Common negative three Positive 12 Common negative three negative sex come a positive three positive sex composite three


Similar Solved Questions

5 answers
Assignment5: Problem 8Previous ProblemProblem ListNext Problempoint) If 5x2 + 3x+xy = 2 and y(2) = -12, find J (2) by implicit differentiation:J() = -3.5Preview My Answers Submit Answers You have attempted this problem time: Your overall recorded score is 0%. You have unlimited attempts remaining:
Assignment5: Problem 8 Previous Problem Problem List Next Problem point) If 5x2 + 3x+xy = 2 and y(2) = -12, find J (2) by implicit differentiation: J() = -3.5 Preview My Answers Submit Answers You have attempted this problem time: Your overall recorded score is 0%. You have unlimited attempts remain...
5 answers
Consider the cegion 6nclosed by" Y=Cos(bx) and tho X-cxic whece O<xe $ 1) Find centroid of (egion (_
Consider the cegion 6nclosed by" Y=Cos(bx) and tho X-cxic whece O<xe $ 1) Find centroid of (egion (_...
5 answers
A girl delivering newspapers covers her route by traveling 6.00 blocks west, 4.00 blocks north, and then 2.00 blocks east: (a) What is her resultant displacement? blocks(b) What is the total distance she travels? blocks
A girl delivering newspapers covers her route by traveling 6.00 blocks west, 4.00 blocks north, and then 2.00 blocks east: (a) What is her resultant displacement? blocks (b) What is the total distance she travels? blocks...
4 answers
Point) (az What the equation of the plane passing through the points (3,0,0) , (0,1,0), and (0,0,2](b) Find the volume of the region bounded by this plane and the planes € 0,y = 0,and ~ = U. volume
point) (az What the equation of the plane passing through the points (3,0,0) , (0,1,0), and (0,0,2] (b) Find the volume of the region bounded by this plane and the planes € 0,y = 0,and ~ = U. volume...
5 answers
Use FTC Lo find tba defiatw oF 4 42_1 F) J e @x-l } Culculae Ft) ane dtemmim if 11 is inunasiyj] 0r ceexeascg at Y-|
Use FTC Lo find tba defiatw oF 4 42_1 F) J e @x-l } Culculae Ft) ane dtemmim if 11 is inunasiyj] 0r ceexeascg at Y-|...
2 answers
Thbatet Hru nre #ppolying Dcteutnibe Ienartlr uuth ILEAd nbatTTETA EAlcf [LE LatHCdineTr Aenlla =IJ (Z)l Nate tbt tat Jou nre apoltnz: DetcM4ne Lhe #pcr brlow #bubeletic oure& &n ~ Eing thatet NMeaynbore JDu #urk: tbc *iite (alTEC diiz Idack 024| Acconing [
thbatet Hru nre #ppolying Dcteutnibe Ienartlr uuth ILEAd nbat TTETA EAlcf [LE Lat HCdine Tr Ae nlla =IJ (Z)l Nate tbt tat Jou nre apoltnz: DetcM4ne Lhe #pcr brlow #bubeletic oure& &n ~ Eing thatet NMeaynbore JDu #urk: tbc *iite (alTEC diiz Idack 024| Acconing [...
5 answers
(10 Points) Decide ifthe functions f(c) and g~) = &9 52 + 7are even, odd, or Leither: (b) (10 Foints) Find the domain of the function f(z)
(10 Points) Decide ifthe functions f(c) and g~) = &9 52 + 7are even, odd, or Leither: (b) (10 Foints) Find the domain of the function f(z)...
5 answers
B2.9 If R = 120 Q and the reading of ammeter is 24 mA are given for the following circuit; the electromotive force (in V) is:7.29.513.111.75.4
B2.9 If R = 120 Q and the reading of ammeter is 24 mA are given for the following circuit; the electromotive force (in V) is: 7.2 9.5 13.1 11.7 5.4...
5 answers
Rectangular box of heighty having square base with sidelength * Is to be made_ If the area ofthe Dox I5 294 Units Ihen; t0 maximize the volume must be units andy must De units Then the maximum volume
rectangular box of heighty having square base with sidelength * Is to be made_ If the area ofthe Dox I5 294 Units Ihen; t0 maximize the volume must be units andy must De units Then the maximum volume...
1 answers
A mining cart is pulled up a hill at $20 \mathrm{~km} / \mathrm{h}$ and then pulled back down the hill at $35 \mathrm{~km} / \mathrm{h}$ through its original level. (The time required for the cart's reversal at the top of its climb is negligible.) What is the average speed of the cart for its round trip, from its original level back to its original level?
A mining cart is pulled up a hill at $20 \mathrm{~km} / \mathrm{h}$ and then pulled back down the hill at $35 \mathrm{~km} / \mathrm{h}$ through its original level. (The time required for the cart's reversal at the top of its climb is negligible.) What is the average speed of the cart for its r...
1 answers
Give an example of a vector field $\mathbf{F}$ such that $\nabla \times \mathbf{F}$ is a function of $x$ only.
Give an example of a vector field $\mathbf{F}$ such that $\nabla \times \mathbf{F}$ is a function of $x$ only....
5 answers
ImageJ File Edil Font ResultsDo6o 19 Iines copled t0 clipboardIA411x9,73cm (2187*2335)RGB L9MB Ja (75" Ladder AlwNI Hindlll AlwNI HindlliUncutResuts Angle Length 3.050 8.317 3.583 3.983 200 '650 250 750 6.333 900 7.367 217 800 833 267 5.967 1667 8.08} LJcm10.1000,10.10 00,35-55
ImageJ File Edil Font Results Do6o 19 Iines copled t0 clipboard IA 411x9,73cm (2187*2335)RGB L9MB Ja (75" Ladder AlwNI Hindlll AlwNI Hindlli Uncut Resuts Angle Length 3.050 8.317 3.583 3.983 200 '650 250 750 6.333 900 7.367 217 800 833 267 5.967 1667 8.08} LJ cm 10.10 00,10.10 00,35-55...
5 answers
Draw the resonance hybrid and the other two resonance structures (always include formal charges if the atom is not neutral): Of all structures (including the one given) , label the major and minor contributorResonance Hybrid:
Draw the resonance hybrid and the other two resonance structures (always include formal charges if the atom is not neutral): Of all structures (including the one given) , label the major and minor contributor Resonance Hybrid:...
4 answers
L(4 pts) Find the volume of the solid in the first octant bounded by 2 = 12 82 and T + y _ 2F1 = (4 pts) Use polar codrdinates to calculate K" 6 (14) dydr.2sin ( rdrdO calcnlates a area of a region given m ecn(2 pts) The integral T|polu coordinates . Sketch the region.
L(4 pts) Find the volume of the solid in the first octant bounded by 2 = 12 82 and T + y _ 2 F1 = (4 pts) Use polar codrdinates to calculate K" 6 (14) dydr. 2sin ( rdrdO calcnlates a area of a region given m ecn (2 pts) The integral T| polu coordinates . Sketch the region....
4 answers
5) Solve the following differential equation that satisfies the given condition_dy dz2x + sec?€ ~X(o) = -5 2y
5) Solve the following differential equation that satisfies the given condition_ dy dz 2x + sec?€ ~X(o) = -5 2y...

-- 0.020684--