Question

use a graphing utility to graph the function and visually determine the intervals over which the function is decreasing, increasing or constant and make a table of values to verify whether the function is increasing, decreasing, or constant. f(x)=x^2/3

Answer 1

What calculator are you using? TI-89?

Answer 2

84 plus

Answer 3

hmm I think that's fairly similar. Do you know how to take a derivative?

Answer 4

nope :(

Answer 5

it's okay! there's just a couple ways to do this. the easiest way is to take derivatives however, we can do it another way! give me a second to get familiar with the TI-84

Answer 6

ok!

Answer 7

okay so first thing you need to do is graph the equation. You can do this by pressing the y='s button on the upper left that will bring up a screen that looks something like:
/y1:
/y2:
/y3:
and so on.

f(x) is just another way to say Y so you just type in your equation after /y1= like so:
/y1=x^(2/3)
Your variable button is right next to the green alpha button, I think. So you are going to press the variable button to enter the x.

now click the window button i think it's right next to the Y= button

set xmin=-10
set xmax=10
set ymin= -10
set ymax= 10

The reason I chose those values is because it should give you a clear picture of what your equation is going to look like! As you graph more equations you will get better and better at choosing a window set.

now click the graph button with is on the upper right I think.
that will give you a nice picture of the graph.

As you can see the graph is increasing. You know this because, the further as you increase the x values, the y values increase also.

Next up is to make the table. if you wanted you could just plug in x values to the equation y=x^(2/3) and make a table that way. But I know a shortcut that will save you a lot of hand work and yield the same result!

You need to get to the table settings menu. I think that it is a secondary function of one of the buttons on the top of your calculator it should say tbl settings in blue or something like that.

once there change the setting "table start" to -5

Now you need to get to the table. I think the table menu is under the secondary function of your graph button. if not, it should be easy to find.

What you see now is a table representation of the graph y=x^(2/3)
so you will see x values starting from negative five and there corresponding y values.

from there all you do is copy down what that table says!

hopefully the directions were clear enough! let me know if you have a question!

Answer 8

Also, if it were my homework I would probably make the table from -3 to 3 but that is up to you.

Answer 9

did that work for you?