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Math Help - Intermediate Value theorem, zero between 2 and 3

  1. #1
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    Intermediate Value theorem, zero between 2 and 3

    Use the intermediate value theorem to show that f(x) = -x^4 + 3x^3 - 2x + 1 has zero between 2 and 3

    I did
    a=2, b=3

    so

    f(a) = -(2)^4 + 3(2)^3 - 2(2) + 1
    = -16 + 24 - 4 + 1
    = -20 + 25
    = 5

    f(b) = -(3)^4 + 3(3)^3 - 2(3) + 1
    = - 81 + 81 - 6 + 1
    = -87 + 82
    = -5

    Is this correct?
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  2. #2
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    Quote Originally Posted by mwok View Post
    Use the intermediate value theorem to show that f(x) = -x^4 + 3x^3 - 2x + 1 has zero between 2 and 3
    a=2, b=3 so
    f(a) = 5 & f(b) = -5
    Is this correct?
    Yes the calculutions at correct. But so what?
    You need to explain what all that proves and why?
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  3. #3
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    Quote Originally Posted by Plato View Post
    Yes the calculutions at correct. But so what?
    You need to explain what all that proves and why?
    Hint to Plato: is this function continuous? Why? Notice that the Intermediate Value Theorem can finish your proof instantly, given that f(x) is satisfies its hypotesis.

    Regards,
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  4. #4
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    Quote Originally Posted by Plato View Post
    Yes the calculutions at correct. But so what?
    You need to explain what all that proves and why?

    Well, both 2 and 3 does NOT produce the zeroes...it produces 5 and -5 but the question is stated in a way that it DOES produce zeroes......how?
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  5. #5
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    Quote Originally Posted by mwok View Post
    Well, both 2 and 3 does NOT produce the zeroes...it produces 5 and -5 but the question is stated in a way that it DOES produce zeroes......how?
    The point is that because one is negative the other positive then by the intermediate value theorem, zero being between then, must be a functional value of a continuous function.

    Quote Originally Posted by Rafael Almeida View Post
    Hint to Plato: is this function continuous? Why? Notice that the Intermediate Value Theorem can finish your proof instantly, given that f(x) is satisfies its hypotesis.
    Rafael Almeida, with all due respect, I donít think that you have the experience to correct me. What I clearly was trying to do was to guide the poster to an understanding of his/her own
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  6. #6
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    Rafael Almeida, with all due respect, I don’t think that you have the experience to correct me. What I clearly was trying to do was to guide the poster to an understanding of his/her own
    Dear Plato,

    I am sorry, I never meant to. Now I see what happened, I mistook your username for mwok's. I though the username Plato started the topic.

    To clarify things, the tip was to mwok. And surely, I don't have neither the experience nor the reputation to correct anybody in here, particularly a poster like you. I'm more a learner than a tutor and I hope to help where I can while I work out my learning process with the help of people like you.

    So, again, sorry for the misunderstanding.

    Sincerely,
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  7. #7
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    Ah, I get it now. Thanks guys!
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