find-the-extreme-values-of-the-function-on-the-interval-and-say-where-they-occur-gxx-1-x-5-2-leq-x-l

Question

Find the extreme values of the function on the interval and say where they occur.
$$g(x)=|x-1|-|x-5|,-2 \leq x \leq 7$$

Katelyn Chen · Accepted Answer

for this question were given. G of X is equal to the absolute value of X minus one minus absolute value of X minus five on interval from negative to as lost unequal to acts which is listener equal to step in. So just start off with were asked a graft ist and then found extreme Ghalia. So we are extreme values are absolute maximum your absolute minimum. So if we look at our function, you can see their absolute maximum is up here that four from interval from from 5 to 7. So we can say that after maximum is four. Um, but 27 and then we also need to look for are absolute minimum so we can say that an absolute minimum is negative floor from native 2 to 1.

Katelyn Chen · Answer

first question were given. The function F of X is equal to the absolute value of maximize two, plus the absolute value of explosive three on the interval where 95 disaster English X, which is Lester. But if I so we are asked to look for any extreme allergies and so we can say, Well, we have a absolute maximum are absolutely mom. So if you look at a graph, you can see whatever absent maximum at this point over here a lot 5 11 So it was the absolute maximum was 11 at X is equal to five and then we can also say that are absolute Menlo is over here, which is five on negative on that interval. Full name free to so five, but no there 3 to 2. It&#x27;s so these are answers

Matt Just · Answer

Okay, so here we have a function G of X equals X minus one minus X minus five. Absolute value and access between negative two and seven. Okay, so we need to think about what this function actually is. Well, we used the fact that absolutely of X minus one is X minus one. If X is bigger than one and one minus X. If extra juice say less than or equal one. And then similarly, for X minus five, this is going to be X minus five if X is bigger than five. But it&#x27;s going to be five minus X if X is less than or equal to five. And so we have all of these sort of conditions past so we can look saying between Wait. Yes, I like when ex is lessening called one. And in between, uh, one in five and then obviously after five. OK, sergey of x legal&#x27;s. So if x is less than or equal to one, then Jia vex is just one minus x minus five minus x. So she&#x27;s in scratch. Work one minus X minus five minus x. Well, this is just going to be negative for Okay, so Jax is gonna be negative for if X is less than or equal to what now X is bigger than one, but less than or equal to five. Then Jia vexes X minus one minus five minus x. So it&#x27;s gonna be to X the cease of X minus a negative X, give me two X and they were gonna have minus one minus five, so it looks like to x minus six. And then if X is bigger than five, what are we gonna have? We&#x27;re gonna have X minus one minus X minus five says ex mind sex, which is Europe and then minus one minus a nine to five is positive for Yes, Very interesting function here. So if we look at the derivative, the derivative is going to be cage. Keep private. X is zero X is less than one in zero. Effects is bigger than five. Men is going to be, too Yes, access between one and five. So we see that it had X equals one. And at X equals five. The derivative is undefined. Good. So two critical points X equals one and X equals five. And so if we look at the graph of this function Years. One, two, three, four, five. Okay, okay, so next is bigger than five. We have four. There&#x27;s negative for for So our function looks like this town. Okay, so there&#x27;s there&#x27;s not going to be okay, so are derivatives undefined at one at five. So that&#x27;s where potentially our backs and men will occur. And so we see the G of That&#x27;s just one more thing. It&#x27;s, uh, met before. Gee, if I&#x27;ve is for so you have an absolute Men late for in Absolute Max of four and that&#x27;s it. Men actually occurs for all values. Less than one. And absent Max occurs for all values of X greater than by

Doruk Isik · Answer

in this fellow were given a function f or this absolute polio explained to plus absolute volume x three. I&#x27;m using a dish on online order. You could do the same thing. This is what the function looks like. This is how it behaves. This is and given interval E 20 Alina maximum ones sporting to or we actually could elect fortunate given in points at Nate five minutes off. So when excess negative by we find the punchline die and when is what expire? We point a bunch more 11 and we also from this crab See that we get a minimum at that insurance off. One X is between two and negative three. Function value is ftz fine. And this is the minimum so graphically. Okay, that&#x27;s the minimum. And after 11 is the facsimile of dysfunction. So this is the maximum and again, graphically, this Poland is the message

Matt Just · Answer

all right here. You know G of X equals X squared Times Square ead of five minus six. So let&#x27;s go and take the derivative because we want the critical point says to meet two X spirit of five minus X plus X squared over, actually minus because of the chain rule Teo Square to five month sex. The derivative of skirt. If I My sex is one over two square to find money, sex times negative one and we can simplify this a good bit. So this is if I multiply the top modern by, say, too square to find my sex to get a common denominator We&#x27;LL have for x times five minus x minus X squared all over too square to five minus x And so, if I want to you prime to be zero than I want Kayla&#x27;s multiplies out. This is twenty x minus for X squared. Minus X squared is your, uh oh, this is twenty X minus five X squared, like in factor out of five ex. And when I was left with for ah minus X so X is zero R X is for and then also G prime can be un defiant. And that happens. The Nexus five. Okay, so critical points at zero for and fast. So let&#x27;s show where she is increasing and decreasing. So have zero for five. So put it like a g prime. Okay, so there&#x27;s gonna be some point where G prime is on to find right. And that&#x27;s going to be how when X is greater than five. And also ji is going to be on to find there. So, undersigned over here, uh, the nexus is less than zero cheap crime. So in the new are just looking the numerator here, the denominators always going to be positive. Jeff, if X is less than zero, this is going to be negative. But this is going to be positive. So it&#x27;s going to be negative. And then between zero and for this is going to be negative, huh? Sorry, this can be positive, and this is still going to be positive. And then between four and five, this is going to be negative. That&#x27;s going to be positives. That b negative g This decrease saying increasing, decreasing and person to find over here, so decreasing between negative infinity and zero increasing between zero and four and then decreasing between four and five. And so good. We have local men&#x27;s well, we can include five is a local men and zero is a local men. So zero zero zero gin&#x27;s your refugee and then five. We also get zero for our value. So local men&#x27;s of zero at X equals zero. Technicals five. And actually, this is going to be our absolute men. And that&#x27;s easy to see because this is always greater than or equal to zero. So if we reached zero, that has to be the absolute men. And then we also have this local Max at four with the value of sixteen man Lucy. Yes, it does actually are absolute Max as well, because it is a unique point. Um, where? Yeah, it&#x27;s a unique, absent maximums. This is actually, um, we actually have a actually, no, we don&#x27;t have an absolute maximum. Okay, so we don&#x27;t have the absolute maximum because, well, this function is decreasing from infinity. This way. So it&#x27;s going off to infinity. Esos excuse to mice Infinity. This function is going to infinity, so no absolute maximum. But we do have an absolute minimum. The zero occurring it zero in five

Linh Vu · Answer

So when did you sketch the graviton function? Yeah, from minus 21 from honest Jew. 271 Jew 3456 and seven. So energetic. Can this one? When did you make a table that gotta do with the accident? Why? So when extra good Germans too with a minister here about a ministry. Absolute miners and minister Here we will go together minus seven. So we get the dream on a seven. So we get it on with ICO To Manus far. That&#x27;s one value on when X it&#x27;ll to one. And now it doesn&#x27;t become zero on get this one will become Ah one minus. Ah Fire. It will be minus far. So becomes a man as far as well. And when? Mexico Jew. Five. When exactly do five here. And then we should get Geico. Thio doesn&#x27;t become zero and isn&#x27;t five minutes when we fall. So the farmers, they got you far. And when Mexico Jew. Seven, seven months. One will be six minus seven minus. Phi will be Jew. So it will be for his Well on. It was giant. You do everything upon him. We should have the calf. Looks like from Minister. We have one is far from here. You only went to one and then after from five 12 to 5. So they were getting good too far. So yeah. No. Yeah, I know it looks like this. So, Elizabeth, with a photograph in a function here and from this craft, and we see that the function will have the, uh, absolute men. Um, thanks. And er minus 2 to 1 on absolute max on the banks in, uh, from 5 to 7, and that&#x27;s pretty different.

Problem

Find the extreme values of the function on the in…

Problem 72 Hard Difficulty

Find the extreme values of the function on the interval and say where they occur.
$$g(x)=|x-1|-|x-5|,-2 \leq x \leq 7$$

Answer

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Joel Hass, Christopher Heil, Przemyslaw Bogacki

University Calculus: Early Transcendentals

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University Calculus: Early Transcendentals

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Joel Hass, Christopher Heil, Przemyslaw Bogacki

University Calculus: Early Transcendentals