# Thread: Intermediate Value Theorem

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

2.

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

Originally Posted by Ackbach
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.

5. Originally Posted by TheDougheyMan
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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