Question

(文)給出下列四個(gè)命題:

①若函數(shù)f(x)=a(x³-x)在區(qū)間()上為減函數(shù),則a＞0;②函數(shù)f(x)=lg(ax+1)的定義域是{x|x＞};③當(dāng)x＞0且x≠1時(shí),有l(wèi)nx+≥2;④若M是圓(x-5)²+(y+2)²=34上的任意一點(diǎn),則點(diǎn)M關(guān)于直線y=ax-5a-2的對(duì)稱點(diǎn)M′也在該圓上.

所有正確命題的序號(hào)是___________.

Answer 1

解析：①f′(x)=a(3x²-1)=3a(x+)(x),

∵x∈(,)時(shí),f′(x)＜0,∴a＞0,①正確;

②當(dāng)a＞0時(shí),定義域?yàn)閧x|x＞},

當(dāng)a＜0時(shí),定義域?yàn)閧x|x＜},②不正確;

③x＞0時(shí),lnx∈R,∴l(xiāng)nx+≥2或lnx+≤-2,③不正確;

④圓心為(5,-2),適合y=ax-5a-2,即直線過圓心,∴④正確.∴①④正確.

答案：①④