##### find all of relative extrema in calculus

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a. g'(x) = 3x^2 - 27 = 0

3(x^2 - 9) = 0

x^2 - 9 = 0

x = +/- 3

g(-3) = 54

so, there is a **relative maximum at (-3, 54)**

g(3) = - 54

so, there is a **relative minimum at (3, -54)**

b. Here's the graph

When it states all relative extreme alphabetically what does that mean? On the graph which graphing software did you use and what was entered to show the graph provided? When I tried using graph 4.2.2 I was so confused because I did not know how or what to enter. Can you provide steps on this as well for future graphs I will need? Much thanks Vincent you are a god sent:-)

Hi Denise. I'm not sure what they mean by alphabetically. I've never heard that before in connection with relative extremes. As far as the graph is concerned, I use an online graphing calculator called meta-calculator. Just google it. There are many others, but I like that one. You just enter the function as y = x^3 - 27x and it will draw it. Then I just used microsoft paint to edit it and label the maximum and minimum points.

Hope that helps.

OH, wait a second. You mean algebraically, not alphabetically :) No wonder I was confused. Algebraically just means calculating it mathematically without graphing it.

OMG LOL I am so sorry thank you so much. I am going to try it with the graph 4.2.2 version to see if it works. Let you know if it works.

I think when it comes to graphing this is where it gets tricky, from the above answer how do you know or arrive at y=x^3-27x?

the function is g(x) = x^3 - 27 x. that is the same as y = x^3 - 27x. the graphing calculator only accepts y, it does not recognize g(x) or f(x) or any other notation like that.

Hello again vincent I have tried entering this function on the graphing tool you provided and also the one that I have. For some reason I am not coming up with what you show in the attachment. Is there a way to provide an attachment showing the steps of you graphing this function?

On the meta-calculator website you click on the graphing calculator option. In box number 1 you type in the formula y = x^2 - 27x. Then scroll down to the bottom. On the right side you should see a blue button with the word "Graph". Click on that and it will produce the graph on a new page. On the right side of that page you need to adjust the Y-Min and Y-Max value so that the curve will fit on the graph enough to reveal the relative maximum and minimum parts of the curve. Y-Min: - 60 and Y-Max: 60 should be enough. Then you will see the whole curve.

Hope that helps.

I'm sorry, I meant type in the formula y = x^3 - 27x

Ok I finally got it to look like your does, is there a way to show these points labeled within this software?

No. I had to save the graph and then use an editing program like Microsoft Paint or any other photo editor.

Okay thank you so much vincent. You have been so patient with me in this process. I just want to make sure that I understand the answers as well so that I can become comfortable with calculus. You have been great in answering all of my questions. Thanks so much.

Okay thank you so much vincent. You have been so patient with me in this process. I just want to make sure that I understand the answers as well so that I can become comfortable with calculus. You have been great in answering all of my questions. Thanks so much.

Okay thank you so much vincent. You have been so patient with me in this process. I just want to make sure that I understand the answers as well so that I can become comfortable with calculus. You have been great in answering all of my questions. Thanks so much.

I don't konw why this repeated three times lol. Quick question, when I click Complete Question can I still view it later?

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