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本文对一个最值问题的一种解法进行改进,帮助同学们深化理解这种解题的方法,并且用改进的解法推广两个问题.希望对同学们的学习有所启发.1.原解法呈现题1已知二次函数f(x)=ax2+bx+c(b>a)对于任意实数x都有f(x)≥0,求M=a+b+c/b-a的最小值.解M=a+b+c/b-a=3(b-a)+(4a-2b+c)/b-a=3+f(-2)/b-a.
This paper improves a solution to a most value problem to help students to deepen their understanding of this problem-solving method and to promote the two problems with an improved solution in the hope of enlightening the students’ learning.1. Problem 1 It is known that the quadratic function f (x) = ax2 + bx + c (b> a) Find the minimum value of M = a + b + c / ba for any real number x with f M = a + b + c / ba = 3 (ba) + (4a-2b + c) / ba = 3 + f (-2) / ba.