find-the-absolute-maximum-and-minimum-values-of-each-function-on-the-given-interval-then-graph-th-25

Question

Find the absolute maximum and minimum values of each function on the given interval. Then graph the function. Identify the points on the graph where the absolute extrema occur, and include their coordinates.
$$F(x)=-\frac{1}{x^{2}}, \quad 0.5 \leq x \leq 2$$

Katelyn Chen · Accepted Answer

for this question were given effort. Faxes equals and I did one over X scored on just 10.5 was lost Earnings X, which is lost or equal to two and were asked to find absolute extreme values. And so these air absolute maximums in the absolute minimum. So several flights. We can rewrite this as negative. Extend negative, too, which makes it easier for a Caesar parable. So then we have primer backs is equal to it. Let&#x27;s see if we can multiply this by negative to to get this to be colisee two x two Negative one dish is equal to two X, and so in a two over, accessible to zero and then one x equal to what was most by both sides but X just get to 00 So there&#x27;s just no critical numbers. And so gun based on this information me know. OK, so we have to overtax. So we&#x27;re going to say there&#x27;s no critical numbers, so we can just have while we have fo 0.5, we should big f. So he says he&#x27;s there, silent soon at those absent maximums minimums. So obey absorb what 50 to negative 1/0 500.4 squared, which is equal to mate a four into the next we have off of to What does Eagleton into 1/2 Squared is equal to number 1/4. So when you say they&#x27;re absolute, you know, occurs out there before being a absolute maximum must rewrite this as negative 0.250 after a maximum prison ended 0.25 So you next We need to grasp this. So we have I wonder, if I were X squared on the interval. No one wants that we have 2.5. Choose this English Extra sister equals two and so we can see the absolute minimum occurs. It&#x27;s negative. Four. House A maximum occurs at negative 0.25

Katelyn Chen · Answer

this question were given the function after vax Eagle two X squared minus one onto interval from night of one is not able to x, which is lost people to to when were asked to find the absolute extreme bodies which is our absolute maximum in are absolutely love. So start off with when I find any critical number is so we know that this is a derivative of your backs off prime of X is equal to using. All right, let&#x27;s see, We can take our two new friends and we drop our drop Our power to get us to X and two X is equal to zero an exit ticket 07 state critical numbers are X equals zero. So when we&#x27;re finding our absolute maximum minimums organised our side links and then our people about loose. So we have s of negative one which is equal to maybe one squared minus one which is just equal to zero. It&#x27;s up from zero which is equal to zero squared. My swan, which is equal to native one we have to, which is equal to two squared minus 12 is equal to three and so we can see that are absolute minimum is, uh, to negative one, their absolute acts. Mom, is that three? Now? The next thing we should do is we need to cross this so we can go to does my Swede X squared minus one on the interval from We have nice one. His last three equal to X, which is Lester unequal to to And so we can see that we have our absolute minimum at zero negative one and in an absolute maximum that 23 So we so this will be our answer.

Katelyn Chen · Answer

for this question, we given ffx people tonight of one over X and we&#x27;re Asif on absolute extreme rallyists or absolute maximums and minimums on the interval from than you to disaster able to act such as lost in equal to negative one. Now another dysfunctions continuous A. There&#x27;s no minimums or maximums on this interval so we can go ahead. Just plug in our numbers. So we have a evening two is equal to this will be wilder and I get one learning to which is equal to 1/2. Then we have us with 91 which is equal to maybe have one over negative one which is equal to one. So we have our absolute then mom. But what half under absolute maximum, not one. The next time we need to do is in photographed this So we have made it one over X. I&#x27;m a *** too, which is of Leicester equal extra success in equal to named of one. And so actually weaken your half has people to 0.5. So consider this over here is 0.5 so we can find out our absolute minimum is that 0.5 and absolute maximum is that one

Katelyn Chen · Answer

for this question were given the function after vaccines able to for my sex cube drivel. Full night of two was Austin Able Switches Lesson. People toe one were asked upon absolute extreme values, which are absolute maximum, absolute minimum. So sterile flights we can find a critical numbers. We find a derivative of F of X, which is equal to neither three X squared. And so we need to find critical Number said is when you&#x27;re three x great, it&#x27;s equal to zero. It gets expertise. You go to zero X equal to zero. So we note our critical number is acceptable to zero so we can find out c f of our silence. Anarchic remembers. We&#x27;ve got your 20 to 4 minus 92 cubed, which is equal to four plus eight to see. Go to 12. We have one physical, two for minus one cube, which is equal to three. That&#x27;s what we have often zero she was before my hero Que, which is just equal to four. It was so consider absolute mineral. His three. Your absolute lacks wound. I was 12. Next we&#x27;re asked a graph this so we have. Let&#x27;s see quarrel mice X cubed from May Give to is less than or equal Teoh X, which is a strangle 21 So we&#x27;ve got aircraft. You can see there are minimum because right there at 13 your maximum absent maximum because the negative to 12 it&#x27;s like it&#x27;s absolutely at wise Eclipse Syria Absolute Lex, move where is equal to 12?

Katelyn Chen · Answer

for this question. We&#x27;re asked if on outside maximums and in moments of after vexed with 2/3 X minus five on the domain negatives of taking access lasted about a free. So Sarah Foot, let&#x27;s find the first survey tive of our backs off perplex. Did you just get us 2/3? Because we know that zero is never equal to 2/3. We know that there is no critical numbers. So another absolute laxman off so little because you&#x27;re 2/3 acts Nice. Five contestants to me, we&#x27;ll have to be at the size of her domain. So we have after a night or two with your ghost Magner 19/3. We have f of three, which will get us think this three. And so Then they saw this. We know that this is going to be our absolute No, no, in this over here is going to be our absolute lacks. Um So the next thing you&#x27;re us to do is we are asked to graph this in, so we have sex. So I see we have a Rolex deep allergic 2/3 X minus five. Through our graph looks something like this. You have what grass e That scene you have ALS call aside If I were here are line and you say that this ever Here&#x27;s corpus ineptitude in the 19/3. This point over here 3 93 in So these are answers.

Katelyn Chen · Answer

for this question. Region of access. It was a scary to four months X Square, dutiful from later to which is lost. Unable to acts which is listener equal to one, we&#x27;re has to find absolute extreme values, which are after Maxwell&#x27;s are absolutely ones. Does this start off? Let&#x27;s we need to find new possible cripple values so we have drew. Prime effects is equal to assuming is your priority channel. So we get, um, let&#x27;s see. We have 1/2 square roots before my sex squared times the derivative of this, which is over inside, which is just times neither two packs. Let&#x27;s see or choose a cancer out. So we&#x27;re left with native X over square roots of four mice export. So we know the night of X over square root of four miles. X squared is equal to zero. Never exited with zero X is equal to zero. So next we need to put me in our values. So we have after neighbor. Do you wanna go to its equal to stories of four minus 92 squared physical to score of four months, for which is equal to zero? They only have a city of one. She was escorted for my so one squared, which is equal to the score rays of three. Lastly, we have geo zero, which is equal to stories of for my zero square. Which did you go to to So we have our absolute minimum that zero under absolute maximum to So we graft this. So we have Let&#x27;s see screws of for my sex squared from I look to if you&#x27;re suggesting it was extra system able to one, you can see that would have the absolute minimum, but zero in our absolute maximum not to. So this is our answer.

Problem

Find the absolute maximum and minimum values of e…

Problem 25 Medium Difficulty

Find the absolute maximum and minimum values of each function on the given interval. Then graph the function. Identify the points on the graph where the absolute extrema occur, and include their coordinates.
$$F(x)=-\frac{1}{x^{2}}, \quad 0.5 \leq x \leq 2$$

Answer

Absolute maximum: -0.25 absolute minimum: -4

Related Courses

University Calculus: Early Transcendentals

Related Topics

Discussion

Top Calculus 1 / AB Educators

Anna Marie V.

Heather Z.

Kayleah T.

Samuel H.

Calculus 1 / AB Courses

Precalculus Review - Intro

Functions on the Real Line - Overview

Recommended Videos

Watch More Solved Questions in Chapter 4

Video Transcript

Joel Hass, Christopher Heil, Przemyslaw Bogacki

University Calculus: Early Transcendentals

Anna Marie V.

Heather Z.

Kayleah T.

Samuel H.

Precalculus Review - Intro

Functions on the Real Line - Overview

What do you need help with?

Textbooks

Ask a question

Courses

AI Tutor

Absolute maximum: -0.25 absolute minimum: -4

University Calculus: Early Transcendentals

Anna Marie V.

Heather Z.

Kayleah T.

Samuel H.

Precalculus Review - Intro

Functions on the Real Line - Overview

Joel Hass, Christopher Heil, Przemyslaw BogackiUniversity Calculus: Early Transcendentals

Anna Marie V.

Heather Z.

Kayleah T.

Samuel H.

Joel Hass, Christopher Heil, Przemyslaw Bogacki

University Calculus: Early Transcendentals