5

Thls is similar to Section 3.7 Problem 16:For the function h(x)--X_3xl+ISx+(l)_ Kecp determine the absolute maximum and minimum values on the interval (0,,2}: decim...

Question

Thls is similar to Section 3.7 Problem 16:For the function h(x)--X_3xl+ISx+(l)_ Kecp determine the absolute maximum and minimum values on the interval (0,,2}: decimal place (rounded) (unless the exact answer has Iess than decimals) Answer: Absolute maximumAbsolute minimumHint: Follow Example bymbolic olmatuno hab

Thls is similar to Section 3.7 Problem 16: For the function h(x)--X_3xl+ISx+(l)_ Kecp determine the absolute maximum and minimum values on the interval (0,,2}: decimal place (rounded) (unless the exact answer has Iess than decimals) Answer: Absolute maximum Absolute minimum Hint: Follow Example bymbolic olmatuno hab



Answers

In Problems $37-64$, find the absolute maximum value and absolute minimum value of each function on the indicated interval. Notice that the functions in Problems $37-58$ are the same as those in Problems $13-34$ $$ f(x)=x^{4}-2 x^{2}+1 \text { on }[0,2] $$

Or given affects is equal to yeah 15 X square minus one half x cubed. Uh And were also given that the interval is from 0 to 30. So we need to check these endpoints because you could have an absolute max occur at those values. Um So the other theme in the problems to actually just take the derivative, which is following the power rule two times 15 is 30. Now it's extra the first because you're supposed to subtract one from the exponents something over here, three halves, X squared and you're supposed to set the derivative equals zero. Now from here, what I would actually do is factor out um maybe a three and an X from the problem because three times 10 and give me 30. Um And then by factoring out that one half we're three had three times one half is three half still X. And what we can get you will have a relative extreme X equals zero. We were already going to check that in but then setting the other piece 10 minus one half X equal to zero. Um I would add one half over and then multiply everything by two. So the other piece to check is 2010 times too is 20. So we need to go back to the original problem, plug in zero for X. 20 for X. And then the other end point which was 30. Now the zero I can do in my head because if exit zero up here than anything times zero is just going to zero. Um Otherwise I need to plug in 20 and from both these exits and then 30 and from both those exits. So that's what I'm doing right now. I'm using a calculator. I don't know if you can hear me plugging away here but when I did 20 I got 2000 again just plugged in um 20 and from both exes. And then when I plugged in 30 and from both exes I got zero again. So when you compare the critical numbers which is the exodus 20 to the end points I got the largest value was 2000. So that must be my absolute max at X equals 20. So the absolute max value is 2000 at X equals 20. And then these other two, you know the phrase is just the absolute men is zero and then you get the X. Five X equals zero. And it also happens that X equals 30. But the main thing is that the men value is zero and the max value is 2000.

For this problem, we are asked to find the absolute maximum and absolute minimum of the function F of x equals x squared times the square root of two minus x on the interval from 0 to 2. So we've already found that this function has critical points at zero and at 8/5. So what we can see then is that zero is trivially already one of the end point. So we are already going to be evaluating that 8/5 is indeed in our interval. So we want to evaluate our function at zero, which is going to give us a zero. He also wants to evaluate our function at to the other end point, which is going to give us zero. And then we want to evaluate our function at 8/5. Now doing that, We get about 1.619 or a very ugly expression that cannot be simplified further.

Yeah. For this problem we are asked to find the absolute maximum and absolute minimum of the function F of X equals E to the power of x minus three acts on the interval from 0 to 1. So we have already found where the critical values for this function are. Specifically, we have a critical number at X equals log of three where lawn of three or log. Actually I should be careful. I am referring to the Natural law algorithm. Uh The numerical value of the natural algorithm of three is about 1.09. So that is actually outside of our domain. So we don't care about that. Which means we just need to evaluate our function at zero and at one now F zero is going to be each power of zero minus zero. So that's going to be one And f of one is going to be E -3 And we know that E is about 2.7. Um so we can easily see that E -3 is going to be negative number, it's going to be less than one, so we can see that One is going to be our max and E -3 is going to be our minimum.

Well, given this function defined pads for X squared minus one, half X tuned. And we only care about the interval from zero to age. So when it gets time to it, we are going to check these endpoints as well as the critical numbers for the absolute extreme. So what we need to do is find the derivative and we're going to use the power room or we multiply the exponent by the coefficient. Subtract one from the exponents. Yeah, three minutes, one is two and we have to set that equal to zero. So if I were doing this problem, other what I would do is factor out just an X. Keep it simple and you'd have eight minus three halves X. So this ex for a critical number could be zero but it was already one of our endpoints. So we're going to check that anyway. And then a minus three has X equals zero. So I would probably just uh had three has x 20 multiply the two over and then divided by three, you know, to get rid of each piece. Um So my critical numbers would be 16 3rd to check out. So what we need to check for the absolute extreme is first of all er and points 0.5 of eight but we also have to check out f of 16 3rd. Well this first one would be really easy because if I plug in zero for all those values, I'm going to get zero. Um Otherwise I need to go back to the original function, plug in those values for X columns are looking at for X squared minus one, half execute and I need to plug 16 3rd. Um um I don't know if you have a professor that would prefer to see the fraction or the rounded answer, but then you also have to check with eight so confidence when I did that, I got zero. So what I just found out by testing these values, whether you write down the 1024 over 27 or this 37 9 to 6, that's an absolute max. And then these other values because of the smallest between the two of them, that would be your absolute mint. Now the phrase is the absolute min value is zero and then you can get the X. Values and it occurs at at X equals zero or eight. Um but we mostly care about the men value of zero and then max values this one.


Similar Solved Questions

5 answers
Lob /3 Name &riaAAlack Where and Intevvals rela tive extrema Find all decrea cing - increasing OY Fcx) IsRox) X7 e"3
Lob /3 Name &riaAAlack Where and Intevvals rela tive extrema Find all decrea cing - increasing OY Fcx) Is Rox) X7 e" 3...
5 answers
In Exercises 25-30, find the critical points and test for relative extrema. List the critical points for which the Second-Partials Test fails. 29. f(x; y) = x/3 "2/3
In Exercises 25-30, find the critical points and test for relative extrema. List the critical points for which the Second-Partials Test fails. 29. f(x; y) = x/3 "2/3...
5 answers
1 1 1 CeceGle 1 0L Ganei J Uuns 1 1 1 1 cncckn * COUM L4ice LHooticasu
1 1 1 CeceGle 1 0L Ganei J Uuns 1 1 1 1 cncckn * COUM L4ice L Hooticasu...
5 answers
Express the integrand as a sum of partial fractions and evaluate the integrals. 1 X+6 dx 2x3 18xRewrite the integrand as the sum of partial fractions. X+6 2x8 18xEvaluate the integrals X+6 f dx = 2x8 _ 18x
Express the integrand as a sum of partial fractions and evaluate the integrals. 1 X+6 dx 2x3 18x Rewrite the integrand as the sum of partial fractions. X+6 2x8 18x Evaluate the integrals X+6 f dx = 2x8 _ 18x...
5 answers
EXAMPLE 1Differentiate4x3 sin(x)SOLUTION Using the Product Rule and this formula, we have4x3 dxsin(x) dxdx4x3sin(x)
EXAMPLE 1 Differentiate 4x3 sin(x) SOLUTION Using the Product Rule and this formula, we have 4x3 dx sin(x) dx dx 4x3 sin(x)...
5 answers
Chapter 21 Problem 014Three particles are fixed on an x axis_ Particle of charge 91 is at x = and particle 2 of charge 92 is at x = +2 If their net lectrostatic force on particle 3 of charge Q Is to be zero what must be the ratio 91/92 when particle 3 Is at (a) x = +0.369a and (b) +1.57a?(a) NumberUnits(b) NumberUnits
Chapter 21 Problem 014 Three particles are fixed on an x axis_ Particle of charge 91 is at x = and particle 2 of charge 92 is at x = +2 If their net lectrostatic force on particle 3 of charge Q Is to be zero what must be the ratio 91/92 when particle 3 Is at (a) x = +0.369a and (b) +1.57a? (a) Numbe...
5 answers
DuttaELleF5 MaTmrClmtAaamtSelect tne @losestcroice [O YCurjndo LYTYPFTHELeTTeRinTHEBLANK(AHUAWEI
Dutta ELle F5 Ma Tmr Clmt Aaamt Select tne @losestcroice [O YCur jndo LYTYPFTHELeTTeRinTHEBLANK(A HUAWEI...
5 answers
GT25% 5801 PM Houra: Mhintican 5ecends:7) A posslbk sze mack CkLryc'iutl: &anu 9I5 cntoIk [clkrII: 34)-6) Wathcrlc Grlhr Trtl1mcctl follov ing pwntyQucednntTr ratixI0 Tk &rminant 1A.oftha matris ^ i(- %7( C#€ -B#(-} 9) D#kZ -TuctiontIzio /4 mkmih lolluxing Ticnh:-mulmn ulcumiom 7-97=12 Whan u cqutions Uc wnkn nun 4-O)
GT 25% 5801 PM Houra: Mhintican 5ecends: 7) A posslbk sze mack Ck Lryc'iutl: &anu 9I5 cntoIk [clkrII: 34)-6) Wathcrlc Gr lhr Trtl1 mcctl follov ing pwnty Qucednnt Tr ratix I0 Tk &rminant 1A.oftha matris ^ i (- %7( C#€ - B#(-} 9) D#kZ - TuctiontIzio /4 mkmih lolluxing Ticnh:-mulmn ...
5 answers
Part BWhat is the displacement amplitude? Use 1.42x105 Pa for the adiabatic bulk modulus of air:AZdA=mSubmitRequest AnswerPart CAt what distance is the sound intensity level 35.0 dB ?AZdm
Part B What is the displacement amplitude? Use 1.42x105 Pa for the adiabatic bulk modulus of air: AZd A= m Submit Request Answer Part C At what distance is the sound intensity level 35.0 dB ? AZd m...
5 answers
Determine whether the relation represented by the directed graph given above Is reflexive, symmetric; anti-symmetric; andlor transitive?Select all that apply:Select one or more:a.Anti-symmetricb: None of theseReflexived. SymmetricTransitive
Determine whether the relation represented by the directed graph given above Is reflexive, symmetric; anti-symmetric; andlor transitive? Select all that apply: Select one or more: a.Anti-symmetric b: None of these Reflexive d. Symmetric Transitive...
5 answers
Which ofthe elements listed below has thehighest first ionization energy? A) He B) Ne C) Ar D) Kr E) Xe
Which ofthe elements listed below has thehighest first ionization energy? A) He B) Ne C) Ar D) Kr E) Xe...
5 answers
A weather forecast model which assume two states; sunny and rain, Suppose that p = 0.6 and 4 =0.4 are neither both equal to zero nor both equal then lim P(X, = V) =
A weather forecast model which assume two states; sunny and rain, Suppose that p = 0.6 and 4 =0.4 are neither both equal to zero nor both equal then lim P(X, = V) =...
5 answers
The lack of pigmentation in humans, called albinism, is theresult of a recessive allele a and a normal pigmentation is theresult of its dominant allele A. Two normal parents have an albinochild.- Determine the probability that their next child is albino- if they have two more children, what is the possibility thatone of those children will be albino and the other will have normalpigmentation?
The lack of pigmentation in humans, called albinism, is the result of a recessive allele a and a normal pigmentation is the result of its dominant allele A. Two normal parents have an albino child. - Determine the probability that their next child is albino - if they have two more children, what is ...
5 answers
Conpitmarulac vres nu nuc57actruJuobCddlngpundhocaumntDmuinntrrendanJcannKeunchon incruid I/77Eureo47FanouWttmOFuctolapptoumutahy $pnr mcketnmordcttrcnardCAt Aaaby noarormolch {Ueer ncetThotC5t
conpit marulac vres nu nuc57 actru JuobC ddlng pund hocaumnt Dmuin ntrrendan Jcann Keunchon incruid I/77 Eureo 47Fanou WttmO Fuctol apptoumutahy $ pnr mcket nmordct trcnard CAt Aaa by noarormolch {Ueer ncet Thot C5t...
5 answers
86.6 The Implicit Function TheoremProblem 6.22_ Assume that one proves the implicit function theorem without applying the inverse theorem _ Show the inverse function using the implicit function theorem.
86.6 The Implicit Function Theorem Problem 6.22_ Assume that one proves the implicit function theorem without applying the inverse theorem _ Show the inverse function using the implicit function theorem....
5 answers
Approximatc Mnm live decimal pluces using tle line izition L(z) or fG): }at @ IU and usc calculator t0 compute thc percentalge error(Usc decima| nolalion Give CutaISuctfour decima pliccs-Thc pcrcemtaye crrUr
Approximatc Mnm live decimal pluces using tle line izition L(z) or fG): }at @ IU and usc calculator t0 compute thc percentalge error (Usc decima| nolalion Give CutaISuct four decima pliccs- Thc pcrcemtaye crrUr...

-- 0.020271--