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  1. MHB Apprentice

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    #1
    I have a continuous function h(x) and the inequality h(b)<=0<=h(a). Can I apply IVT?

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  3. Indicium Physicus
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    #2
    Well, what are the hypotheses of the IVT? Are they satisfied in your case?

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    #3 Thread Author
    Quote Originally Posted by Ackbach View Post
    Well, what are the hypotheses of the IVT? Are they satisfied in your case?
    Isn't it just that h(x) is continuous and if u is a number between h(b) and h(a),
    h(b) < u < h(a), then etc etc. I didn't think I could, but I just wanted to see a variation of it.

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    #4
    Quote Originally Posted by TheDougheyMan View Post
    Isn't it just that h(x) is continuous and if u is a number between h(b) and h(a),
    h(b) < u < h(a), then etc etc. I didn't think I could, but I just wanted to see a variation of it.
    Exactly right. So you can conclude that there is a $c \in (a,b)$ (I'm assuming $a<b$) such that $h(c)=0$.

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