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使用均值定理证明

问题

已知 f, left parenthesis, x, right parenthesis, equals, 2, start superscript, x, end superscript, minus, start text, s, i, n, end text, left parenthesis, pi, x, right parenthesis.
小李试图证明等式 f, prime, left parenthesis, x, right parenthesis, equals, start fraction, 1, divided by, 4, end fractionminus, 2, is less than, x, is less than, minus, 1 上有解.
小李的证明完整吗? 如果不, 为什么?
下面是小李的证明:
指数和三角函数在域上的所有点都是可微和连续的, 而minus, 2, is less than or equal to, x, is less than or equal to, minus, 1f 的域内.
因此, 根据中值定理, f, prime, left parenthesis, x, right parenthesis, equals, start fraction, 1, divided by, 4, end fraction 在区间 minus, 2, is less than, x, is less than, minus, 1 上一定有解.
选出正确答案:
不会做了?
不会做了?