函數(shù)f(x)=mx*x+(m-1)x+1在(-∞,1]上為減函數(shù),則m的取值范圍是多少?

熱心網(wǎng)友

函數(shù)f(x)=mx^+(m-1)x+1在(-∞,1]上為減函數(shù),則m的取值范圍是多少? 解:①m=0時(shí)f(x)=-x+1,在(-∞,1]上為減函數(shù)②m≠0時(shí)函數(shù)f(x)=mx^+(m-1)x+1是開(kāi)口上的拋物線(xiàn),m＞0且對(duì)稱(chēng)軸x=-(m-1)/2m≥1,∴1-m≥2m(注:m＞0),∴0＜m≤1/3綜上所述:0≤m≤1/3