在中学数学教材里,有这样一道例题:设a、b、m都是正数,ab,证明:aba+mb+m.它的证明是不难得到的.有趣的是它的物理意义是“糖水加糖会更甜”的浅显道理.从函数观点看,该例题表明f(x)=a+xb+x在[0,+∞)上是严格单调递增的;从几何观点看,过O(0,0)、A(b,a)的直线的斜率小于过O(0,0 In the middle school mathematics textbook, there is such an example: Let a, b, m be positive, ab, prove: aba + mb + m. Its proof is not difficult to get. What’s interesting is that its physical meaning is “sugar ”The sweetening will be sweeter." From a functional point of view, this example shows that f(x) = a + xb + x is strictly monotonically increasing on [0, + ∞); from a geometric point of view, O (0) ,0), A(b,a) The slope of the line is less than O (0,0)