Zeros of a Function

We shall now use infinite partitions to sketch the proofs of three basic results, called the Intermediate Value Theorem, the Extreme Value Theorem, and Rolle's Theorem. The use of these results will be illustrated by studying zeros of continuous functions. By a zero of a function f we mean a point c where f(c) = 0. As we can see in Figure 3.8.5, the zeros of fare the points where the curve y = f(x) intersects the x-axis.

Figure 3.8.5