【Chia Chung】評論

<Solution>   (95年 數學甲)V先前分析：f(x)=x5+2x4-x3-5x2+3一、f'(x)=5x4+8x3-3x2-10x=x(x-1)(5x2-13x+10)二、x=0 &1時 有極值三、f"(x)=20x3+24x2-6x2-10------------------------------------------------------(A) (k為正整數)=>False<Solution>limx->∞{f(k)/f(k+100)}limx->∞{[k5+2k4-k3-5k2+3]/(k+100)5+..........}=1_______(Answer)------------------------------------------------------(B) =>Truelimx->1 {f(x)-f(1)}/(x-1)=f'(1)=0 -----------------------------------------------------(C) 函數f在區間遞增=>False∵f"(1)>0 =>凹口向上-----------------------------------------------------(D) 若x≥0 ，則f(x)≥0=>True∵f"(1)>0 =>凹口向上，且x=1時f(1)=0 (局部極小值)--------------------------------------------------------(E)在坐標平面上f(x)與直線y＝3恰有兩個交點=>True∵f(0)=3  f'(0)=0，y=3剛好與f(x)相切於點(0,3)Answers：(B)(D)(E)