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Math Help - Intermediate Value Theorem question

  1. #1
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    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.
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  2. #2
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    Quote Originally Posted by phys30 View Post
    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.
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  3. #3
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    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?
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  4. #4
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    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 )
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  5. #5
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    Ok, so to get this straight, I'll just find where x=0?
    Thank you for all your help!
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