Intermediate Value Theorem

On page 193 of the textbook, the intermediate value theorem is discussed. For the intermediate value theorem why do you think it is necessary for the signs of f(a) and f(b) to be different in order to guarantee there is a zero between a and b.

If it is the case that the signs of f(a) and f(b) are the same, does that mean the function f(x) cannot have a zero between a and b? Explain.

The following link may be helpful:

https://www.mathsisfun.com/algebra/intermediate-va…

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