設(shè)二次函數(shù)f(x)=(k減4)x^2+kx (k屬于R) 對(duì)任意實(shí)數(shù)x,f(x)小于等于6x+2恒成立,數(shù)列{an}滿(mǎn)足an+1=f(an) ...
設(shè)二次函數(shù)f(x)=(k減4)x^2+kx (k屬于R) 對(duì)任意實(shí)數(shù)x,f(x)小于等于6x+2恒成立,數(shù)列{an}滿(mǎn)足an+1=f(an) (1)求函數(shù)f(x)的解析式和值域 (2)試寫(xiě)出一個(gè)區(qū)間(a,b)使得當(dāng)a1屬于(a,b)時(shí),數(shù)列{an}在這個(gè)區(qū)間上是遞增函數(shù) 急
解:f(x)=(k-4)x^2+kx<=6x+2
(k-4)x^2+(k-6)x-2<=0
k-4<0且:判別式=(k-6)^2+8(k-4)<=0得k=2
f(x)=-2(x-1/2)^2+1/2,值域{y|y<=1/2}
an+1=f(an)=-2an^2+2an
an+1-an=-2an^2+an>0
得0