Question

solve for x

x-3*cuberoot(x) = 0

Answer 1

I was using wolfram alpha to graph, and it's only showing two of three roots. It seems to think the domain is only x larger or equal to 0.

Answer 2

http://www.wolframalpha.com/input/?i=x+-+3x^%281%2F3%29+for+real+numbers

Answer 3

Is it (x-3)*cuberoot(x) = 0?

Answer 4

sorry,
\[x - 3\sqrt[3]{x}\]

Answer 5

the graph on wolfram does not match the information I get from looking at intervals of increasing, decreasing, local extrema, concavity, domain, ...

Answer 6

It's going to be difficult to isolate x here

Answer 7

factor out the cube root
\[\sqrt[3]{x}(\sqrt[3]{x^2} - 3)\]

Answer 8

You gave me the impression that the x -3 wasn't in parentheses

Answer 9

so you are trying to figure out why wolfram has a different graph then the one you came up with?

Answer 10

it isn't...

Answer 11

Even so, you still have an x lingering

Answer 12

myininaya: yes - exactly

Answer 13

ok let me see what i come up with
i will scan and post ok?

Answer 14

thanks... I attached what I

Answer 15

have

Answer 16

there are three x values that work, but only two solutions are valid

Answer 17

why is the negative sol. not valid?

Answer 18

x = 0, 3sqrt 3, -3sqrt 3

Answer 19

heromiles,
\[0-3\sqrt[3]{0} = 0\]

Answer 20

\[-3\sqrt[3]{3\sqrt{3}}= -3\sqrt[6]{27} = -3(3^3)^{1/6} = -3\sqrt{3} \]
and
\[-3\sqrt[3]{-3\sqrt{3}} = 3\sqrt[6]{27} = 3(3^3)^{1/6} = 3\sqrt{3} \]

Answer 21

What about the graph? Does it match your solutions?

Answer 22

your graph looks fine

Answer 23

the TI-84 Plus matches, but not wolfram alpha

Answer 24

Thanks for checking myininaya. Any thoughts on why wolfram disagrees?

Answer 25

no i dont know its weird
i was like maybe i need to zoom in but no wolfram has the wrong graph

Answer 26

even my calculator agrees with us

Answer 27

You graphed two solutions, right?

Answer 28

you mean two x-intercepts?
that doesn't matter
i still have the same shape

Answer 29

Yes, two x-intercepts

Answer 30

I solved it a bit differently though

Answer 31

did you factor out an x instead?

Answer 32

myininaya: I think your second derivative should be
\[\frac{2}{3x^{5/3}} = \frac{2}{3x\sqrt[3]{x^2}}\]
So there would be a sign change at 0, right?

Answer 33

No, I cubed both sides to get rid of the cube root

Answer 34

you are right cruffo

Answer 35

I ended up with x(x^2 - 27) = 0

Answer 36

but still this doesn't give us the graph wolfram has

Answer 37

what is the point of the second derivative lol

Answer 38

concavity :)

Answer 39

i know it tells if the function is concave up and concave down lol but it doesn't really change the graph

Answer 40

very pretty

Answer 41

no :), of course. 2nd derivative just gives us a little more information to work with.

Answer 42

I thought the original question was to find x....

I simply used algebra to find x, then I plugged in the values of x and found that x = 0, sqrt 27

Then I graphed it. What more do you need to do?

Answer 43

he wants to know why his graph is different from wolfram

Answer 44

so do I :)

Answer 45

you are totally right and wolfram is wrong

Answer 46

I wanted to assign this problem for homework, but if wolfram is gonna be that way about it...

Answer 47

Cruffo, you graphed it manually?

Answer 48

yep

Answer 49

Thank you all for your help.

Answer 50

wait cruffo

Answer 51

wolfram is confused about the cube root of -1
i think it thinks it imagary
do -1-cuberoot(-1)

Answer 52

wow!!!

Answer 53

or i mean
do -1-3cuberoot(-1)

Answer 54

cube roots of unity?????

Answer 55

both should be imagary based off wolfram let me try

Answer 56

yep

Answer 57

anyway to force it to work only over the reals...

Answer 58

cuberoot(-1)=0.5+ci
where c is some irrational number

Answer 59

Why are you so dependent on wolfram alpha for graphing?

Answer 60

I'm not, but my students like to use it

Answer 61

he proabably don't want his students second guessing themselves since there are not confident in math

Answer 62

Very correct (and it's she by the way :), and I try to help them with the correct commands to use. I don't mind that they use a computer, I like it. In fact, I prefer them to use a computer to a calculator. But, this will cause the majority of them to give up. I can't seem to figure out how to force wolfram to work only on the real number without errors...

Answer 63

me neither

Answer 64

oh well. I'll just give the warning.

Answer 65

i'm a she too just so everyone knows

Answer 66

Contact Wolfram and point out the error

Answer 67

so don't call me sir or boy

Answer 68

lol

Answer 69

Yes!!! :) Again, thank you all for your help.

Answer 70

this doesn't make sense
x^3=-1
wolfram gives the solution x=-1

Answer 71

i mean its right but it can't do (-1)^(1/3) so how can it solve this

Answer 72

i wonder what method it used to solve x^3=-1

Answer 73

Hilarious

Answer 74

For graphing , I prefer my TI N-spire

Answer 75

I'll send an email regarding the issue to wolfram, along with these other test.

I'm not too familiar with Mathematica, but I think it works "symbolically", but not sure...

I prefer SAGE. Very nice open source program for symbolic math. You can specify the field you want to work on.
http://www.sagemath.org/

Answer 76

ok i don't trust wolfram anymore

Answer 77

thanks for letting me know about this lol

Answer 78

Geogebra is a pretty good program

Answer 79

Well, you should always try to verify answers at least qualitatively, right. This is actually a really good example of that fact!

I always try to find those sneaky functions to use, but this one crept up on me :)

Ohh... I like geogebra!!! I should have though about that one.

Answer 80

we built programs
its our fault they make mistakes

Answer 81

Geogebra does a good graph of this problem

Answer 82

I graphed it on geogebra...it graphed correctly and it finds the cube root of -1 correctly

Answer 83

nice

Answer 84

lets find a mistake in the program lol

Answer 85

i will save it for later
i need to go to bed

Answer 86

The only question is, can it isolate and solve for x

Answer 87

good night myininaya

Answer 88

not sure, heromiles. I haven't used geogebra for that.

Answer 89

If there's a way, I'll figure it out

Answer 90

there is a "root" command, but not a "solve" command

Answer 91

root command uses newton's and false position methods

Answer 92

it finds the positive and negative root, but not the root at 0 using newton's method. It will find the root at 0 using false position.

Answer 93

well, I need to finish up the hints for the homework problems. Good night!!

Answer 94

There's also a solutions command apparently. Have to try it out.

Answer 95

Well, I think this is only for version 4.0

Answer 96

Actually, it has a solutions and solve command, which is great.