## Calculus 8th Edition

There is a condition missing if we want to apply the Intermediate Value Theorem, f must also be continuous for this to be true. Construct a piecewise function, such as $f(x)=\left\{\begin{array}{lll} 1, & & x < 2\\ -1 & & x \geq 2 \end{array}\right.$ which fits the conditions of the statement, but there is no c in the interval [1,3] for which f(c)=0.