一、选择题
1. 题目
若函数\(f(x) = x^3 - 3x\)在区间\([0,2]\)上的最大值为\(M\)，则\(M\)的值为：
A. \(-2\)
B. \(2\)
C. \(0\)
D. \(3\)
解答
首先，对函数\(f(x) = x^3 - 3x\)求导得到\(f'(x) = 3x^2 - 3\)。令\(f'(x) = 0\)，解得\(x = \pm 1\)。在区间\([0,2]\)内，只有\(x = 1\)是可能的极值点。
接下来，我们计算\(f(1) = 1^3 - 3 \times 1 = -2\)，\(f(0) = 0^3 - 3 \times 0 = 0\)，\(f(2) = 2^3 - 3 \times 2 = 2\)。
比较这三个值，发现\(f(2) = 2\)是最大的。因此，\(M = 2\)。
答案：B
二、填空题
1. 题目
若复数\(z = a + bi\)（其中\(a, b \in \mathbb{R}\)）满足\(|z - 1| = |z + 1|\)，则$a = _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________