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(1)若x₁=-1,x₂=2,求函數(shù)f(x)的解析式;

(2)若|x₁|+|x₂|=,求b的最大值;

(3)若x₁＜x＜x₂,且x₂=a,函數(shù)g(x)=f′(x)-a(x-x₁),求證:|g(x)|≤a(3a+2)².

(文)如圖,N為圓x²+(y-2)²=4上的點(diǎn),OM為直徑,連結(jié)MN并延長(zhǎng)交x軸于點(diǎn)C,過(guò)C引直線垂直于x軸,且與弦ON的延長(zhǎng)線交于點(diǎn)D.

(1)已知點(diǎn)N(,1),求點(diǎn)D的坐標(biāo);

(2)若點(diǎn)N沿著圓周運(yùn)動(dòng),求點(diǎn)D的軌跡E的方程;

(3)設(shè)P(0,a)(a＞0),Q是點(diǎn)P關(guān)于原點(diǎn)的對(duì)稱點(diǎn),直線l過(guò)點(diǎn)P交曲線E于A、B兩點(diǎn),點(diǎn)H在射線QB上,且AH⊥PQ,求證:不論l繞點(diǎn)P怎樣轉(zhuǎn)動(dòng),恒有.