已知函數(shù)f(x)的導(dǎo)函數(shù)f'(x)是二次函數(shù),當(dāng)x=±1時(shí),f(x)有極值,且極大值為2,f(2)=-2.
(1)求函數(shù)f(x)的解析式;
(2)若函數(shù)y=|f(x)-k|-1有兩個(gè)零點(diǎn),求實(shí)數(shù)k的取值范圍.
(3)設(shè)函數(shù)h(x)=2x
2+(1-t)x,
g(x)=[+h(x)]e-x,若存在實(shí)數(shù)a,b,c∈[0,1],使得g(a)+g(b)<g(c),求t的取值范圍.