必修五必考題目及答案一、選擇題（每題3分，共30分）1.函數(shù)y=f(x)的圖象關(guān)于點(diǎn)(1,2)對(duì)稱，那么f(3)等于多少？A.0B.4C.3D.1答案：B2.若函數(shù)f(x)=x^2-4x+m，且f(1)=-2，則m的值為多少？A.1B.2C.3D.4答案：B3.已知函數(shù)f(x)=2x+3，g(x)=x^2-4x+5，求f[g(2)]的值。A.5B.7C.9D.11答案：C4.若函數(shù)f(x)=x^3-3x^2+2在區(qū)間[1,2]上單調(diào)遞增，則下列哪個(gè)函數(shù)在該區(qū)間上單調(diào)遞減？A.f'(x)B.f''(x)C.f'''(x)D.f(x)^2答案：A5.已知函數(shù)f(x)=x^2-6x+8，求f(x)的最小值。A.-4B.-2C.0D.2答案：A6.函數(shù)f(x)=sin(x)+cos(x)的值域是什么？A.[-1,1]B.[-√2,√2]C.[0,√2]D.[1,√2]答案：B7.若函數(shù)f(x)=x^3-3x^2+2x+1在x=1處取得極值，則該極值是？A.0B.1C.-1D.2答案：B8.函數(shù)f(x)=x^2-4x+m的頂點(diǎn)坐標(biāo)是什么？A.(2,m-4)B.(2,m+4)C.(-2,m-4)D.(-2,m+4)答案：A9.函數(shù)f(x)=|x|在x=0處的導(dǎo)數(shù)是多少？A.0B.1C.-1D.不存在答案：D10.函數(shù)f(x)=x^3-3x^2+2x+1的單調(diào)遞增區(qū)間是？A.(-∞,1)B.(1,+∞)C.(-∞,1)∪(2,+∞)D.(1,2)答案：C二、填空題（每題4分，共20分）1.若函數(shù)f(x)=x^2-6x+8的頂點(diǎn)坐標(biāo)為(3,-1)，則該函數(shù)的對(duì)稱軸方程為________。答案：x=32.函數(shù)f(x)=x^3-3x^2+2的導(dǎo)數(shù)f'(x)為________。答案：3x^2-6x+23.函數(shù)f(x)=sin(x)+cos(x)的周期為________。答案：2π4.函數(shù)f(x)=x^2-4x+5的值域?yàn)開_______。答案：[1,+∞)5.函數(shù)f(x)=|x|在x=0處的左導(dǎo)數(shù)為________，右導(dǎo)數(shù)為________。答案：-1，1三、簡(jiǎn)答題（每題10分，共50分）1.已知函數(shù)f(x)=x^3-3x^2+2，求出f(x)的單調(diào)區(qū)間，并說(shuō)明理由。答案：函數(shù)f(x)的導(dǎo)數(shù)為f'(x)=3x^2-6x=3x(x-2)。令f'(x)>0，解得x>2或x<0，即函數(shù)在區(qū)間(-∞,0)和(2,+∞)上單調(diào)遞增；令f'(x)<0，解得0<x<2，即函數(shù)在區(qū)間(0,2)上單調(diào)遞減。2.已知函數(shù)f(x)=x^2-4x+5，求出f(x)的極值點(diǎn)和極值，并說(shuō)明理由。答案：函數(shù)f(x)的導(dǎo)數(shù)為f'(x)=2x-4。令f'(x)=0，解得x=2，即x=2為極值點(diǎn)。當(dāng)x<2時(shí)，f'(x)<0，函數(shù)單調(diào)遞減；當(dāng)x>2時(shí)，f'(x)>0，函數(shù)單調(diào)遞增。因此，x=2為極小值點(diǎn)，極小值為f(2)=1。3.已知函數(shù)f(x)=|x|，求出f(x)在x=0處的左導(dǎo)數(shù)和右導(dǎo)數(shù)，并說(shuō)明理由。答案：函數(shù)f(x)在x=0處的左導(dǎo)數(shù)為lim(x->0^-)(f(x)-f(0))/(x-0)=lim(x->0^-)(-x)/x=-1；函數(shù)f(x)在x=0處的右導(dǎo)數(shù)為lim(x->0^+)(f(x)-f(0))/(x-0)=lim(x->0^+)x/x=1。因此，函數(shù)f(x)在x=0處的左導(dǎo)數(shù)為-1，右導(dǎo)數(shù)為1。4.已知函數(shù)f(x)=x^3-3x^2+2x+1，求出f(x)的拐點(diǎn)坐標(biāo)，并說(shuō)明理由。答案：函數(shù)f(x)的二階導(dǎo)數(shù)為f''(x)=6x-6。令f''(x)=0，解得x=1，即x=1為拐點(diǎn)橫坐標(biāo)。將x=1代入原函數(shù)，得到f(1)=1，即拐點(diǎn)坐標(biāo)為(1,1)。5.已知函數(shù)f(x)=sin(x)+cos(x)，求