Math help please!

[Evensong]

I'm supposed to sketch the following (I'm majoring in Sociology and I need to pass a calculus course - exam next week - but I'm no mathematician.) I have this typed up in microsoft equation 3.0 but I have no idea how to paste it in here:

f(x)=2x^4-5x^3+3x^2

So far I've been pretty well able to solve some of these, but for this exercise I probably keep ruining the same thing over and over.

1.) Df: x-R
2.) Rf: f(x)-R
3.) Intersection: f(x)=0
4.) zp-x1=0, x2=3/2, x3=1
5.) lim f(x) x->(this is supposed to be infinity standing :D)=8
lim f(x) x->-8=8
6.) stationary points f(x)’=0=8x^3-15x^2+6x and x1=1,3 (approximate) x2=0,58
y1=-0,2 and y2=0,26
I know I’m ruining it here somewhere…
7.) mon. ]-8;0,58[ f(x)’<0 (and on the drawing it should be >0)
]0,58;1,3[ f(x)’<0
]1,3;8(infinity)[ f(x)’>0
8.) inflection points where f(x)’’=0=24x^2-30x+6 ->x1=1; x2=1/4
y1=0; y2=0,12
9.) concave/convex ]-8;0,25[ f(x)”>0 convex
]0,25;1[ f(x)”<0 concave
]1;8[ f(x)”>0 convex
10.)and here’s my table and sketch but it’s in my notebook….at the f’ ]-8;0,58[ my drawing goes down, and, according to this site http://rechneronline.de/function-graphs/ it should be rightly going up…where do I keep getting lost?

Edit: edited a few numbers, my arrow --> got turned into 8s and my 8s are supposed to be infinities

[Woozie]

Clearly you understand pretty well how to do these type of problems. Whatever mistake you made must have been a minor algebraic error like forgetting a sign or whatever. So I'm just going to redo the problem the way you did it and we'll see where we get different answers.

I don't understand your notation with your backwards brackets and semicolons. So it's hard for me to directly address whatever issue you're having because I don't understand what you're saying.

1) and 2)I don't know what Df and Rf stand for and I'm not sure what you're doing here.
3) You need to find where the graph touches the x axis. So you solve for f(x) = 0, as you've already pointed out.
4) are you listing the zeros of your function? If so, x2 = 3/2, not 3/4
Edit: my bad, I read that as 3/4, the first time.
5) Not sure what you're doing here. Are those 8's supposed to be infinity? I'm assuming that's what you meant by the infinity standing thing.
6)Maybe I screwed up, but I got the stationary points as 0, 0.58, and 1.30, which correspond to y = 0, y = 0.26, and y = -0.20.
Edit: My bad, your commas instead of decimal points confused me. We got the exact same answer.
7) I'm a little confused about what's going on, but it seems you're finding the slopes over the different regions of the graph?
for x in (-∞,0), y' is negative
for x in (0, 0.58 ) y' is positive
for x in (0.58,1.30) y' is negative
for x in (1.30, ∞) y' is positive
8 ) inflections points: I got exactly what you got
9) Concativy
for x in (-∞, 1/4) y'' is positive
for x in (1/4, 1) y'' is negative
for x in (1, ∞) y'' is positive

http://i48.tinypic.com/rcplwn.jpg

Edit: It looks like we got the exact same answer on every single step. Does your sketch look like the graph I posted?

[Ramor]

i'm guessing Df and Rf are domain and range respectively? though i'm with woozie in that i'm unfamiliar with most of your notation but i do end up getting the same answers (and will save the trouble of typing them all out again)

not exactly sure what the problems are that you're having

[Evensong]

Thanks for your help, truly appreciated!
No, I didn't get the same drawing!
I'm not studying in English, so forgive me if I'm not translating these terms correctly. We use commas instead of dots (0,5 is 1/2) and dots when expressing larger numbers like 1.000.000 would be a million.
Df is I think domain of x, so x are Real numbers and Rf might be codomain? Basically, that f(x) also belongs to the domain of Real numbers.
5.) Yes, the 8 is supposed to be infinity.
7.)

for x in (0, 0.58 ) y' is positive

This is where I get negative...
What we do at step 7 is draw a line (number line? no idea how to call it) and then divide it into segments based on the stationary points. So for x stationary points 1,3 and 0,58 we divide the number line into 3 segments: from ]-8;0,58[ meaning all numbers from minus infinity to 0,58 but not including 0,58, which is why the bracket is open...I think, but I'm getting confused as I write!
And then we look for the easiest numbers in that interval, like -1 and -2. We then say x=-1 and calculate the first derivative. So, 8*(-1)^3-15(-1)^2+6(-1) and I get -29, and all we need to know is that it's a negative number, so from -8 to 0,58 the monotony of the slope is negative...it goes down and it should be positive!

10.) Here we make a chart with the columns consisting of all the stationary points, zero places, inflection points and the rows are f", f' and f. For f" we put little + signs if it's convex and - signs if it's concave. For f' we use + if the slopes ascend and - if they descend...and then we put it all together...

Edit: Ok, I see I'm missing a 0 for a stationary point?

[Woozie]

i'm guessing Df and Rf are domain and range respectively? though i'm with woozie in that i'm unfamiliar with most of your notation but i do end up getting the same answers (and will save the trouble of typing them all out again)

not exactly sure what the problems are that you're having

Oh okay, domain and range makes sense.

[Woozie]

You can't go (-∞,0.58 ) because 0 is a stationary point and you just skipped right over it.
You have to go (-∞,0 ) and then (0, 0.58 ).

By plugging in a -1, you've shown that the slope is negative on the interval (-∞, 0) (which is true). Since zero is a stationary point, you have to stop your interval at zero and then try a new point for your next interval, which is (0,0.58 ). Plug in anything in this interval and you'll get a positive number.

Edit: Wow, your notation is way different than here lol. For us, an open interval a to b is (a,b), and a closed interval a to b is [a,b]. I'm starting to understand your notation though.

Edit: Yes, you were missing zero as a stationary point. Sorry, I thought you had zero as a stationary point. Normally when people separate numbers by commas, it means a list of numbers. So when I saw 0,58 I thought you meant "0 and 58". (i.e. I thought you meant 0 and .58 but had forgotten a decimal point in front of the 58 ). I should have noticed that you only had two stationary points instead of three, but I wasn't used to your notation so I was a bit confused x_x

[Evensong]

This is where I usually ruin my math exercises...I just skip over things like negative, positive signs and zeroes.

O.o oh wow! I'm looking at my notebook now and I see the stupidest thing I've done wrong! I just used the quadratic formula for 8x^3-15x^2+6x without factoring the equation. No wonder I lost a zero. I'm so going to fail with something like this...

Thank you for help again! I might still have a question or two, which I'll just post here sometime this weekend!

[Woozie]

Oh, and in English we would call R the codomain in this case. The range would be the set of outputs, which in this case is (-0.202,∞). We typically don't talk about codomains in calculus because the codomain is pretty much always going to be R in calculus. Don't worry too much writing things in our notation. Just tell us in advanced next time so we're not so confused lol

[Evensong]

Don't worry too much writing things in our notation. Just tell us in advanced next time so we're not so confused lol

Thank you! I'll do my best to give an advanced warning, though it's kinda hard when I don't know where our notations differ! ^^

Btw, I see you use an infinity sign here...it would be very nice for me to have one too. Is it on your keyboard or can I find one here? It would look much better than my 8s and be far less confusing (for me at any rate).

[Ramor]

from what i can tell for notations you have open brackets as ]0,1[ we use (0,1), closed brackets are [0,1] for us, same for you?

and of course the different usage of commas and periods which you explained earlier, other than that i think they're the same

[Woozie]

I actually went to microsoft word, looked under symbols, found the infinity symbol, put it into my document, then copied the symbol from the document and pasted it here.

Just type out the word infinity if you can't find the symbol. The 8's threw me off.

[Evensong]

from what i can tell for notations you have open brackets as ]0,1[ we use (0,1), closed brackets are [0,1] for us, same for you?

Yes, the closed brackets are the same. But if you think about it, ours is more logical...I mean, open brackets for open intervals and vice-versa. These are closed too () <- though if you really use your imagination, you could think about it as almost looking like an O and thus an abbreviation for "open!" Well, that's how I'll remember it now.

Woozie, how do you copy and paste Microsoft Equation 3.0 stuff in here? I kept copying it, but it just refused to paste it here.

[Woozie]

Not the equation editor. Go to "insert" and instead of choosing "equations" choose "symbols". Equations wont copy/paste but symbols will.

e.g. ∞€£¥©®™±≠≤

etc

For equations, I use

http://www.codecogs.com/components/e...tioneditor.php

If you're vaguely familiar with LaTex, this is pretty easy to use.

[Eliseos]

You can also use the character map to copy and insert special characters. Start-> Accessories -> System Tools for XP. Some of these you can hold alt and type numbers in on the numpad. For example, Alt + 0178 = ². To use infinity in this way, you'd have to allow hexadecimal input in your registry, but copy and pasting is easy enough and you don't have to worry about messing up your registry.

[Evensong]

•®

I get the all rights reserved but not the infinity when I copied and pasted from Word.

Let me see how the equation looks from that site.

Now I just need to put that attached thumbnails here:-->

Edit: lol, I wanted to ask something about that equation but by the time I type it out it'll be the end of today and I have to get back to finishing a presentation. ; ;

Edit2: http://latex.codecogs.com/gif.latex?...}}+x^{21}+7)dx Ok, I have it, thank you. And I even changed the y to x. Was going to ask if I solved both correctly (the one with the x and the other with the y); but no, I cannot use that LaTex equation formatting.

[Woozie]

http://latex.codecogs.com/gif.latex?...}}+x^{21}+7)dy

Instead of downloading your equation and then uploading it as an attachment, just right click the picture of your equation, copy image location, and then paste it and image tag it with [img][img]. To me, it looks better that way. If you're not familiar with LaTex equation formatting, it's not worth even using this site because it will take forever to type up anything.