17-24-sketch-the-graph-of-f-by-hand-and-use-your-sketch-to-find-the-absolute-and-local-maximum-and-6

Question

$17-24$ Sketch the graph of $f$ by hand and use your sketch to
find the absolute and local maximum and minimum values of
$f$ . Use the graphs and transformations of Sections 1.2 and $1.3 . )$
$$f(t)=\cos t, \quad-3 \pi / 2 \leqslant t \leqslant 3 \pi / 2$$

Clarissa Noh · Accepted Answer

Hi, it&#x27;s Clara. So when you raid here, so here we&#x27;re going to sketch a graph you have. If Steve&#x27;s a number in the Domaine de of a function of the embassy is the and you have four criteria is here. So we&#x27;re gonna draw a graph and just want to love something like this. I&#x27;ll drawn in blue well and from the graph because see that there&#x27;s absolute max and local max both when X is equal to zero and there&#x27;s two local minimum and an absolute minimum when F&#x27;s equals pi and X equals negative pie.

Zachary Watson · Answer

Okay, so tryingto graft the function f of t is equal to co sign t where t must be great angle to negative three pi over two, but is less than or equal to three pi over two Photographed a something. You understand how coastline works with within the unit circle when co sign is coastline of t is equal to zero or when you have a co signer zero I should say gonna have that our effort. Easy, quick, Troy, when you have a co signer pirate too. Effort is going equal to zero. When we have co sign off pie effort, he&#x27;s gonna equal to negative one and have three Piper to f t is gonna be equal to zero once again. So let&#x27;s try and map this out. So we have zero part 20 hi negatively three prior to zero And then the same thing applies for the negative values and negative pirate too is gonna equal to pi to secret deserve negative pies. Equal pirates is equal to zero. Same for I&#x27;m sorry. Negative pilot which is equal to negative lawyer and a key part two is zero. So the guard, basically they look something like this. All right, so it&#x27;s Ah, it&#x27;s just make your weight. So we need to find the local men&#x27;s and Max for this We&#x27;re gonna have actually, in this case is we have this small interval we&#x27;re gonna have in absolute max. Ah, is there one? And then we&#x27;re gonna have to look gas and local max minimums. Ah, pride negative way, You know, so negative by a little.

Oswaldo Jiménez · Answer

here we are going to sketch the graph of the function. Go sign of T. For the argument in the interval from negative three by half. Three by half. Including both endpoints with that craft. We&#x27;re going to find the absolute and local maximum and minimum values of the function. So we&#x27;re gonna use this system here. This coordinate system. We&#x27;re going to do more or less the graph of the coastline function. We know to go send a serious one so we can have something like this. Okay let&#x27;s go sign the here&#x27;s a little bit better than that. And then we have this far here and this bar here more or less. And here we have. The value is included because we have included both in points. The value of negative three by half and three by half zero. Mhm. Sorry. Here see your rock. And this value here is one and this value here We know it&#x27;s -1. That is at this point. The one which is the same as this point here. And as we can see we have here all the elements we can have in terms of extreme extreme A. So we have first we have the absolute maximum value of the function is one, attain it zero. But it&#x27;s also local because if you look any interval Near zero or contain zero. And look at the graph only there again the value you want to see how his value. So F. Has uh an absolute and local maximum and local maximum value. Yeah one at X equals zero. So that&#x27;s the first thing then we have that The minimum value of the function is -1. But it is attained at two points in this case. Let&#x27;s see that these values here here we have by half here we have negative by half. And this number here is by and this number here where we have negative one is by its negative. So this here is negative. That is plus three by half for you. And here is negative three x half. Which is the man we are considering this case. So we attain the the minimum value negative one at two points at by an ad 90 by So if and they are also local because if we take any interval containing the These values the value -1 is the smallest image possible. So f has an absolute minimum value which is also local -1 at the point. Or the numbers X equals negative pi and X equal by And in fact it because he was the function at. Find it under real numbers there will be infinitely many points. Our values where we attain the minimum value in 81. There will also be infinitely many values numbers where we attain the maximum absolute maximum body wants. But in this case we have to train the function to this interval And over there we have this situation if F has an absolutely local maximum value one at zero here. This point here, N F has an absolute and local minimum value in anti juan At two points here and here. So that&#x27;s the behavior of the go sign of T for tea in the interview. From negative three by half and three by half, including both endpoints.

Jennifer Fowler · Answer

Okay, so we&#x27;re asked, It gets the graph of this function on and to determine absolute and local maximum and minimum values. Okay, So noticed that this function is a line. This is a graph of a line. Okay? And we&#x27;re called the wheel. I need two full weeks to draw the line. Right. So we&#x27;re interested in X less than or equal to three. So let&#x27;s find f of three. Except for a minute. Okay, so a three is 1/2 times nine minus one, which is for okay, and then f of zero. Maybe just have another one is negative. One recall to draw the graph of a line, you just need two points. Okay, so let&#x27;s see. 123 1234 Might not be the scale, but as long as we label it, we&#x27;re in good shape. In case of this is the 0.34 And then we have the 0.0 one hand, okay? And we&#x27;re interested in all that Use X less than or equal to three. So this goes on forever. Like this. Okay. So noticed that there is in absolute maximum maximum that half of three. Does he go to four and there&#x27;s no absolute local or local minimum notice also, that this absolute maximum is not a local maximum because in a interval around this, it&#x27;s not even to find on the other side of three, so it&#x27;s not not larger than the function values on the other side of three.

Jennifer Fowler · Answer

Okay, so we&#x27;re asked to skips the function F FX is equal to x square. Um, we&#x27;re exes between zero in two. Okay, so notice that this is a parable. Um, if a plug in zero get zero, but that points, not there. A plug in to I get four. No, 0.24 That point is also not there. Okay. So knows that by definition, this function does not have an absolute maximum. So it has no absolute. And the reason is because this is an open interval, okay? And there and also no local extra. Now, if we had instead looked on the closed interval than it would be guaranteed to have absolute extreme er and they would occur that pinpoints. But this point.

Clarissa Noh · Answer

it&#x27;s Claire&#x27;s with you right here. So if C is the number in the Domaine de of a function up Can FC is the absolute max. If f of cs greater or equal to effort backs for all X and G absolute minimum if FC a smaller equal to f of X for all ex. Indeed, local maximum of FC is greater or equal to an excess. Your seat Local minimum of FC is smaller or great equal when X is in your seat. So we&#x27;re gonna draw a graph below our criteria. So this is why so this is gonna be our absolute maximum. It&#x27;s gonna be negative, too. One, two, three. 12 34 I six were given an equation. Off affects is equal to two minus 1/3 Ex and X is greater or equal to negative too. So we&#x27;re looking at a graph in blue going to look something like this. Start here. Go, go, go, go, go! Go past six. So are absolute, Max. Uh, negative too, is equal to eight. Dirt&#x27;s

Problem

$17-24$ Sketch the graph of $f$ by hand and use y…

Problem 22 Easy Difficulty

$17-24$ Sketch the graph of $f$ by hand and use your sketch to
find the absolute and local maximum and minimum values of
$f$ . Use the graphs and transformations of Sections 1.2 and $1.3 . )$
$$f(t)=\cos t, \quad-3 \pi / 2 \leqslant t \leqslant 3 \pi / 2$$

Answer

$\begin{aligned} \text { Abs }(\max ) \text { and } & \text { local }(\max ) f(0)=1 \\ \text { Abs }(\min ) \text { and } & \text { local }(\min ) f(-\pi)=-1 \\ \text { Abs }(\min ) \text { and } & \text { local }(\min ) f(-\pi)=-1 \end{aligned}$

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$\begin{aligned} \text { Abs }(\max ) \text { and } & \text { local }(\max ) f(0)=1 \\ \text { Abs }(\min ) \text { and } & \text { local }(\min ) f(-\pi)=-1 \\ \text { Abs }(\min ) \text { and } & \text { local }(\min ) f(-\pi)=-1 \end{aligned}$

Biocalculus Calculus for the Life Sciences

Grace H.

Catherine R.

Anna Marie V.

Samuel H.

Precalculus Review - Intro

Functions on the Real Line - Overview

James StewartBiocalculus Calculus for the Life Sciences

Grace H.

Catherine R.

Anna Marie V.

Samuel H.

James Stewart

Biocalculus Calculus for the Life Sciences