$1=1+frac1x^3$ this equation has actually no solutions due to the fact that $frac1x^3$ have the right to never equal 0 and also is undefined as soon as x=0. There fore p is false.


We need to display that there exists one $x$ for which $x = x^3+1$. This is identical to mirroring that $f(x)$ has actually a root, where $f(x) = x^3 - x + 1$. Now use the Intermediate value Theorem.

You are watching: Is there a number that is exactly 5 more than its cube?



"Is over there a number the is precisely one more than its cube?"(In my specific case, this was problem 51 from section 2.4 the Single variable Calculus Concepts and Contexts |4e by James Stewart)

I was just assigned this trouble in a homework assignment because that my calculus class. I took a slightly different approach compared come
Théophile, although making use of the IVT below is most likely the solution which most professors would certainly look for (especially if you were asked this question on a quiz or exam whereby you aren"t permitted a graphing calculator).

You have the right to verify the an $x$ worth which satisfies these parameters exists by graphing $y=x$ and also $y=x^3+1$ as individual functions. Over there is one intersection between these 2 graphs, that offers us the $x$ value which satisfies the equation $x=(x^3)+1$

You deserve to then plug the $x$ value right into the equation $x=(x^3)+1$ to examine the answer.

Note this method serves much more as an aid in conceptualizing this details problem, rearranging the equation $x=(x^3)+1$ and using the IVT to settle for the source is a much more exact means to a solution. That said, i initially discovered it daunting to imagine this scenario, therefore I assumed I"d share my technique in instance anyone else below is struggling in the very same way.


point out
edited january 18 "20 at 22:00
answered jan 18 "20 in ~ 21:31

2155 bronze title
add a comment |

her Answer

Thanks for contributing response to sommos.netematics Stack Exchange!

Please be certain to answer the question. Provide details and also share your research!

But avoid

Asking because that help, clarification, or responding to various other answers.Making statements based on opinion; ago them increase with references or personal experience.

Use sommos.netJax to layout equations. sommos.netJax reference.

To learn more, see our advice on writing an excellent answers.

See more: What Is Better When You Break It Riddle, Riddle : What Is Better When You Break It

Draft saved
Draft discarded

Sign increase or log in in

authorize up making use of Google
authorize up utilizing Facebook
sign up using Email and also Password

Post together a guest

email Required, but never shown

Post together a guest


Required, however never shown

short article Your prize Discard

By clicking “Post your Answer”, you agree come our regards to service, privacy policy and also cookie plan

Not the prize you're feather for? Browse various other questions tagged proof-verification or asking your very own question.

Upcoming occasions
Featured on Meta
room there much more even numbers than odd numbers?
Prove that for every rational number z and also every irrational number x, over there exists a distinct irrational number such that x+y=z
Prove that there is no smallest confident real number
taking care of undefined situation in uniqueness evidence (How come Prove It, Velleman; 5.6, 2)
Is composing "However that is a general reality that..." a precious statement in a proof?
Prove that there are specifically two solutions to the equation $x^3 = x^2$.
permit $a$ it is in a hopeful number. Then there exists exactly one natural number $b$ such the $b ext++ =a$.
Prove by contradiction the a real number that is less than every hopeful real number cannot be optimistic
Prove that there are precisely $phi(p-1)$ primitive roots modulo a element $p$
warm Network concerns much more hot inquiries

concern feed
i ordered it to RSS
question feed To i ordered it to this RSS feed, copy and also paste this URL right into your RSS reader.


stack Exchange Network
site style / logo © 2021 stack Exchange Inc; user contributions licensed under cc by-sa. Rev2021.11.22.40798

sommos.netematics stack Exchange works best with JavaScript permitted

your privacy

By click “Accept every cookies”, you agree ridge Exchange deserve to store cookie on your an equipment and disclose details in accordance v our Cookie Policy.