# Thread: Intermediate Value Theorem question

1. ## Intermediate Value Theorem question

I am trying to show that if f(x)=x^5-2x^3+x^2+2 there exists some real number c such that f(c)=-1.

I would appreciate any help!
Thank you.

2. Originally Posted by phys30
I am trying to show that if f(x)=x^5-2x^3+x^2+2 there exists some real number c such that f(c)=-1.

I would appreciate any help!
Thank you.
If f(x) = -1 then g(x) = f(x) + 1 = 0.

g(x) = x^5 - 2x^3 + x^2 + 3.

Now find values of a and b such that f(a) > 0 and f(b) < 0. Then b < c < a.

3. Oh, I still do not understand!
Can someone help my logic, please?

Can I graph x^5-2x^3+x^2+2 and f(c)=-1, and say that the function is continuous everywhere but especially on [-2,-1], and then find f(-2) and f(-1) and use those values?

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

and you are looking for x where f( x ) = - 1, than it is the same if you write:

x^5 - 2x^3 + x^2 + 2 = - 1 , and that is equal to:

x^5 - 2x^3 + x^2 + 3 = 0 , so solution of this equation is the answer to your question... ( solution can be from R or from C )

5. Ok, so to get this straight, I'll just find where x=0?
Thank you for all your help!