calculus
If f(1) > 0 and f(3) < 0, then there exists a number c between 1 and 3 such that f(c) = 0. Is this true or false?
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True. By the Intermediate Value Theorem, there exists at least one value of c between 1 and 3 for which $f(c)$ = 0. This theorem states that for any continuous function defined on a closed interval, if the function has different values at two distinct points of the interval, then there exists another point in between the two given points, at which the function has the value zero.
