# 2016年考研数二第05题解析

## 题目

$$A. f_{1}(x) \leqslant f_{2}(x) \leqslant g(x)$$

$$B. f_{2}(x) \leqslant f_{1}(x) \leqslant g(x)$$

$$C. f_{1}(x) \leqslant g(x) \leqslant f_{2}(x)$$

$$D. f_{2}(x) \leqslant g(x) \leqslant f_{1}(x)$$

## 解析

$$g(x) > f_{2}(x) > f_{1}(x).$$

$$K=\frac{|y^{”}|}{(1+y^{‘2})^{\frac{3}{2}}} \geqslant 0.$$

$$f_{1}(x_{0}) = f_{2}(x_{0}) = g(x_{0}). (1)$$

$$f_{1}^{‘}(x_{0}) = f_{2}^{‘}(x_{0}) = g^{‘}(x_{0}). (2)$$

$$f_{1}^{”}(x_{0}) < 0.$$

$$f_{2}^{”}(x_{0}) < 0.$$

$$\frac{-f_{1}^{”}(x_{0})}{[1+f_{1}^{‘2}(x_{0})]^{\frac{3}{2}}} > \frac{-f_{2}^{”}(x_{0})}{[1+f_{2}^{‘2}(x_{0})]^{\frac{3}{2}}}.$$

$$f_{1}^{”}(x) < f_{2}^{”}(x) < 0. (3)$$

$$g^{”}(x) = 0. (4)$$

$$f_{1}^{”}(x) < f_{2}^{”}(x) < g^{”}(x) = 0. (5)$$

$$\varphi(x) = g^{‘}(x) – f_{2}^{‘}(x). (6)$$

$$\varphi^{‘}(x) = g^{”}(x) – f_{2}^{”}(x).$$

$$\varphi^{‘}(x) > 0.$$

$$\varphi(x_{0}) = 0.$$

$$\varphi(x) < 0 \Rightarrow$$

$$g^{‘}(x) \leqslant f_{2}^{‘}(x).$$

$$\varphi(x) > 0 \Rightarrow$$

$$g^{‘}(x) \geqslant f_{2}^{‘}(x).$$

$$g(x) \geqslant f_{2}(x).$$

$$g(x) \geqslant f_{2}(x).$$

$$g(x) \geqslant f_{2}(x).$$

$$f_{2}(x) \geqslant f_{1}(x).$$

$$g(x) \geqslant f_{2}(x) \geqslant f_{1}(x).$$

EOF