Question

Find the solutions to 0 < x4 – 6x3 + 6x2 + 9x + 2 by graphing f(x) < x4 – 6x3 + 6x2 + 9x + 2 using technology. I have the graph but I Don't know how to say the solution.

Answer 1

the solution points are those points,where the graph cuts/intersects x axis..

Answer 2

I had somone tell me earlier it me you're simply looking for where the curve is above the x-axis.

Answer 3

oh yes! because of f(x)<x^4.....

Answer 4

yes. that's right.
f(x)>0 means that tha function is over the x-axis.

Answer 5

So am i looking for were the line crosses the x axis or any point above the x axis?

Answer 6

http://www.wolframalpha.com/input/?i=0+%3C+x4+%E2%80%93+6x3+%2B+6x2+%2B+9x+%2B+2
maybe this can help...

Answer 7

http://www.wolframalpha.com/input/?i=graph+y%3Dx^4+%E2%80%93+6x^3+%2B+6x^2+%2B+9x+%2B+2+

Answer 8

as u can see in the graphs posted, the whole function is over the x-axis except for the two points where the graph touches the x-axis

Answer 9

That's funny @helder_edwin this is the exact graph i was referencing when i said " I have a graph." I asked a similar question earlier and the person who helped me told me all points over the x-axis were the solution hence my confusion. So the answer to my question is wherever the points cross the graph?

Answer 10

no. your are not solving and equation. this is an inequation.
the solution is all of \(\mathbb{R}\) but those points where the graph touches the x-axis.

this is because you're solving f(x)>0.

Answer 11

Right, okay I'm finding f(x)?

Answer 12

no

Answer 13

what do u mean by "finding f(x)"?

Answer 14

I'm trying to find what i can set equal to x to make my inequality true?

Answer 15

sorry. it seems the site went down.

Answer 16

yes. but u r finding \(x\). not the funtion.
u r finding the values of \(x\) that makes \(f(x)>0\).

Answer 17

So x is equal to each point that is on both the line and the x axis? (sorry I was waiting for the owl to go away and then relized i had to refresh the page)

Answer 18

no. just the points on the line (x-axis)

Answer 19

O.k. One last thing Very related to the question, Do you have Geo-gebra?

Answer 20

no. what is that?

Answer 21

oh, It's a graphing tool. Free to download and kinda like wolfram. Difference being you can zoom in, save, what have you, the graphs you make. For some reason it's not graphing this particular equation and since i can't zoom in on wolframs graph to see the points, or save the graph, I was wondering if you would know what's wrong with Geogebra.

Answer 22

no idea. sorry :(

Answer 23

to find the points u can use a "good" calculator.
and i believe wolframalfa can do the same: finding the roots of a polynomial