5

Given f(x) = -9 4x? for -1 <x < 1and g(x) = 4 - (x-4)2 for 2 <x < 6.If lis a tangent line for both f and g,then the slope of the tangent line [ equals:A...

Question

Given f(x) = -9 4x? for -1 <x < 1and g(x) = 4 - (x-4)2 for 2 <x < 6.If lis a tangent line for both f and g,then the slope of the tangent line [ equals:Answer:

Given f(x) = -9 4x? for -1 <x < 1and g(x) = 4 - (x-4)2 for 2 <x < 6.If lis a tangent line for both f and g,then the slope of the tangent line [ equals: Answer:



Answers

Find the slope and an equation of the tangent line to the graph of the function $f$ at the specified point. $$f(x)=\frac{1+2 x^{1 / 2}}{1+x^{3 / 2}} ;\left(4, \frac{5}{9}\right)$$

The slope of the tangent line of the function G of X he waas three have events, but one. And we want to see what the slope is at the point. Negatives You negative to you. But we really only put I'm here about the ex year because that's what we're gonna plug in the x coordinate. So let's first find the derivative. So if you remember, uh, my formula for the derivative is the limit. H ghost zero f of X plus each minus effort. Thanks. Oh, so using this plug, expose, agent or function, we get three halfs. It's plus each. That's what minus f of X Surgery of excellence case. So I just switched the signs. The N minus three have X minus one all over each. And when doing these problems, you should definitely get some cancellations. Uh, so Okay, let's try it out. We have 3/2 X plus three has h this one nine ish? Three have sex like this one all over each. So if you don't have to come cancellations going on, something went wrong. So we have three have sex and negative 3/2 X's cancel plus one minus one. Cancel so we're left with. Oh, I forgot my limit. So we should have limit his age goes to zero on the outside of all these. So your limit as each goes to zero 3/2 each overreach, It's just canceled. So our limit is equal to your house. So this is our derivative. So no matter what we plug in, so in this case, we want that you're a bit of a value would be negative, too. No matter what we plug in, our slope is always

Action. Alphabets equals five minus squared. And we want to find the slope of the candle line of this crab at the point three. Negative or so The only thing that we're concerned about here iss the X cause that's what we're gonna play in our derivative. So the derivative gives us the slope of the tangent line at point X. So well, we'll take the derivative using limits. So we hit the limit as h goes to zero f of explosive. Age is I've minus X squared and then we subtracted of X. So we felt the signs minus five. Plus next word all over each. So immediately I see with my eyes cancel. And so what's rewrite this? Use a limited stage zero. And so I'm gonna distribute this negative through. And foil is out on bond stuff. So we get minus X squared, minus two exits minus each square plus x weird all over each. And we see our experts canceled what we want. So this is equal hole in it. It was zero. So now I'm gonna factor out a minus h on the talk so that you cancel with speech on the bottom. So what's left. We have two x waas each. The Fury just canceled. And then we can evaluate the limit by plucking in h equals zero. So you have minds to x off zero, which is negative to X. So the last step is to find what the derivative is at X equal screen. So we have minus two times three, which gives us negative sex as our salute.

We have problem number seven GXE is given help. Access square minus nine and we need to find the slope off tangent at 0.2 comma minus five on this curve. So we have formula for slow attendant at point C x equal to see limit. Delta extends to zero F C plus Delta X minus F C. Divide by Dale Tax. Yes, he is equal to two, so you'll be getting limit. The text tends to zero F off two plus the tax minus F two. Divide by real tax. Now let us plug in the values in our equation. Extra square. That is to place Delta X hold square minus nine minus to risk wire minus nine. Divide by Dell tax. That is limit. The text tends to zero. We have to use, uh, this. We have to open the back. It a plus behold square that is to square, which is four plus dale tax. Hold Squire plus two into two. That is for sale. Tax minus nine and minus four plus nine. Divided by yes, the attacks. Okay, so now, uh, nine and minus nine, minus four and four got canceled out. So this is now limit. Dale text tends to zero this deal taxes choir. So let us right. The mystical taxes common will be having Dale tax plus four divide by deluxe. So Delta X, Delta, will you cancel out? And since, uh, this is real tax approaches to zero. So let's plug in tel tax equal to zero will be getting slow. Pass four. So our answer will be slope for thank you.

I would actually start this problem with the equation that they gave you the three x minus nine Y. Uh -4 equals zero. And the reason why I would work with that is because I would actually add the nine Y to the right side. But I'm going to write it this way And then when you divide everything by 9, 3 divided by nine reduces to 1/3. And then that 49 so I'm just gonna leave it. But what I really care about is the slope of that tangerine is one third. So double check my arithmetic there because then when you go over to the other function defined as x squared minus one and when you're asked to find the derivative of that, Sorry, it's expert -1 x. Um The derivative of that would be two X -1. What we want is the point that gives us a slope of 1/3. Uh So what I would do is add one over and one third plus one will give me four thirds when I divide both sides by two. Or you can multiply by one half, you know, times one over there we go. Uh that would reduce to 2/3 You know, 4 6. So if you go back to the that's the X coordinate for the point, you need to go back up here and figure out what the y coordinate would be. So two thirds of the square would be 4/9 minus two thirds, Which I would get the same denominator again, 2/3 with the denominator of nine to be six nights. So that would be equal to -2 nights for your y coordinate.


Similar Solved Questions

5 answers
LhuchMrior Rocuctenucu ofoycloncnlencBrJCCL?Which comnpounds contain stercxxenters?1-chloropentane II) 2-chloropentune HII) 3-chloropentane IV) 1,2-dichloropcntantb) IIL,IV Lm IL, IVWhich fonns of lactic acid are fonns? Coch cooh cochCOOHL, MW 4, DI DL
Lhuch Mrior Rocuct enucu ofoycloncnlenc BrJCCL? Which comnpounds contain stercxxenters? 1-chloropentane II) 2-chloropentune HII) 3-chloropentane IV) 1,2-dichloropcntant b) IIL,IV Lm IL, IV Which fonns of lactic acid are fonns? Coch cooh coch COOH L, MW 4, DI DL...
5 answers
Write The Question your solution to 18 Moving answer M another mass question decimal places system given save this response Gv*9 8Moving anothe question save 2 response9,.22What is the phase shift?3
Write The Question your solution to 18 Moving answer M another mass question decimal places system given save this response Gv*9 8 Moving anothe question save 2 response 9,.22 What is the phase shift? 3...
5 answers
Due in hours_ 30 minutes. Due Fri 12/06/2019 vertex at (1, 11) . and covertex at (4,Write the equation of the ellipse that has center at (1,PrevicwGet help: Midco] MideoPoints possible: Unlimited attempts_ Message instructor about this question
Due in hours_ 30 minutes. Due Fri 12/06/2019 vertex at (1, 11) . and covertex at (4, Write the equation of the ellipse that has center at (1, Previcw Get help: Midco] Mideo Points possible: Unlimited attempts_ Message instructor about this question...
5 answers
Create a direction field for the differential equation $y^{prime}=(x+5)(y+2)left(y^{2}-4 y+4ight)$ and identify any equilibrium solutions. Classify each of the equilibrium solutions as stable, unstable, or semi-stable.
Create a direction field for the differential equation $y^{prime}=(x+5)(y+2)left(y^{2}-4 y+4 ight)$ and identify any equilibrium solutions. Classify each of the equilibrium solutions as stable, unstable, or semi-stable....
5 answers
If $a$ and $b$ are integers, not both of which are zero, prove that $operatorname{gcd}(2 a-3 b, 4 a-5 b)$ divides $b$; hence, $operatorname{gcd}(2 a+3,4 a+5)=1$.
If $a$ and $b$ are integers, not both of which are zero, prove that $operatorname{gcd}(2 a-3 b, 4 a-5 b)$ divides $b$; hence, $operatorname{gcd}(2 a+3,4 a+5)=1$....
5 answers
DETAILSdx8vX+x-1/6+CAvx-! xs/6+c3 xS/6+c 8 x+ 6 x5/6+€ Vx+xS/6+C
DETAILS dx 8vX+x-1/6+C Avx-! xs/6+c 3 xS/6+c 8 x+ 6 x5/6+€ Vx+xS/6+C...
5 answers
4 points2x1 QA7 Add and simplify: x+3 + x-52x+7 A_ 21-22x2+13x-35 B=E (x+3)(-5)21+7C (x+3)6-5)2x2-3*+21 D_ (x+3)(-5)C 8 B 6
4 points 2x 1 QA7 Add and simplify: x+3 + x-5 2x+7 A_ 21-2 2x2+13x-35 B=E (x+3)(-5) 21+7 C (x+3)6-5) 2x2-3*+21 D_ (x+3)(-5) C 8 B 6...
5 answers
Use the most accurate three-point formula and the following data to approximate f'(2.2)Xi f(xi )2.02.22.42.64.2103.8423.0022.546a3.02b-6.48C3.24d. 6.48e_3.24f.-6.04g: 3.02h_6.04
Use the most accurate three-point formula and the following data to approximate f'(2.2) Xi f(xi ) 2.0 2.2 2.4 2.6 4.210 3.842 3.002 2.546 a 3.02 b -6.48 C 3.24 d. 6.48 e_ 3.24 f. -6.04 g: 3.02 h_ 6.04...
1 answers
Expand. $$(x-\sqrt{2})^{6}$$
Expand. $$(x-\sqrt{2})^{6}$$...
5 answers
A 7180-kg helicopter accelerates upward at 0.80 m/s$^2$ while lifting a 1080-kg frame at a construction site, Fig. 4-68. ($a$)What is the lift force exerted by the air on the helicopter rotors? ($b$) What is the tension in the cable (ignore its mass) which connects the frame to the helicopter? ($c$) What force does the cable exert on the helicopter?
A 7180-kg helicopter accelerates upward at 0.80 m/s$^2$ while lifting a 1080-kg frame at a construction site, Fig. 4-68. ($a$)What is the lift force exerted by the air on the helicopter rotors? ($b$) What is the tension in the cable (ignore its mass) which connects the frame to the helicopter? ($c$)...
5 answers
Determine the values of a.b. such that the following matrix is diagonalizable:A=
Determine the values of a.b. such that the following matrix is diagonalizable: A=...
4 answers
Average systolic blood pressure has a normal distribution withmean of 92 and a standard deviation of 12.a. What is the probability that a single person’s reading willexceed 86?b. What is the probability that the average readings of 36people will exceed 86?
Average systolic blood pressure has a normal distribution with mean of 92 and a standard deviation of 12. a. What is the probability that a single person’s reading will exceed 86? b. What is the probability that the average readings of 36 people will exceed 86?...
1 answers
Find the Fourier series on for(a) , an oddfunction(b) , an evenfunction(c) , using the complexform of the series
Find the Fourier series on for (a) , an odd function (b) , an even function (c) , using the complex form of the series...
5 answers
Suppose forty percent of people in a country carry the coronavirus. Seventy percent of the population are 30 years old oryounger. The probability that a person who is 30 or younger carriesthe virus is 50%. What is the probability that a person who has thecorona virus is older than 30?
Suppose forty percent of people in a country carry the corona virus. Seventy percent of the population are 30 years old or younger. The probability that a person who is 30 or younger carries the virus is 50%. What is the probability that a person who has the corona virus is older than 30?...
5 answers
The vapor pressure of pure benzene at 23 'C 1s 0.1252 atm WVhen 10 of an unknown non-Folatile non-dissociating solute A is dissol cd In 100 bcnzcnc; thc vapor pressure of solution &t 25 C is 0.118 atmn Calculatc the mole ffaction of solute 1n thc soluron0.3190.2520,5624050.107
The vapor pressure of pure benzene at 23 'C 1s 0.1252 atm WVhen 10 of an unknown non-Folatile non-dissociating solute A is dissol cd In 100 bcnzcnc; thc vapor pressure of solution &t 25 C is 0.118 atmn Calculatc the mole ffaction of solute 1n thc soluron 0.319 0.252 0,562 405 0.107...
5 answers
Which of the following is TRUE?Select one:a.All of the alternativesb. The aim of hypothesis testing is to reject the null hypothesisThe null hypothesis is assumed until evidence indicates otherwiseAccepting the null hypothesis proves that the null hypothesis is correct
Which of the following is TRUE? Select one: a.All of the alternatives b. The aim of hypothesis testing is to reject the null hypothesis The null hypothesis is assumed until evidence indicates otherwise Accepting the null hypothesis proves that the null hypothesis is correct...

-- 0.022312--