If a continuous function has opposite signs at two endpoints, a root lies between them. Testing the midpoint and retaining the sign-changing half shrinks the bracket predictably, without using derivatives.连续函数在两个端点异号时，区间内至少存在一个零点。检查中点并保留两端异号的一半区间，就能以确定的速度缩小范围，无需计算导数。
The bracket begins at for . Gold marks each midpoint; the shaded strip retains the half that still contains a sign change.图中对 从 开始搜索。金色点标记中点，阴影保留仍含符号变化的半区间。