week5 college algebra

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week5 college algebra 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:

Intermediate Value Theorem

According to intermediate value theorem, If f is continuous on [a, b]. Then f takes all values between f(a) and f(b). Thus, it will be guaranteed thatthere is a zero between a and b if the signs of f(a) and f(b) are opposite. If they have the same sign, it does not mean they cannot...

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