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1、万全中学高三数学万全中学高三数学(文)(文)同步作业(同步作业(1212)导数的概念)导数的概念一、填空题一、填空题 1、 八个基本求导公式)(C ;)(nx ;(nQ) )(sinx ,)(cosx )(xe , )(xa )(lnx , )(logxa 2、导数的四则运算)(vu )(xCf )(uv ,)(vu )0( v3、曲线在 y=在 x=1 处的切线的方程为 .53123 xx4、 函数yax21 的图象与直线yx相切,则a 5、若曲线的一条切线 与直线垂直,则 的方程为 4yxl480xyl6、设f(x)、g(x)分别是定义在 R 上的奇函数和偶函数,当x0 时, 0.且 g(
2、3)=0.则不等式f(x)g(x)0 的解集是( ) ( )( )( )fx g xf x g x _7、在函数的图象上,其切线的倾斜角小于的点中,坐标为整数的xxy834点的个数有 个。 8、曲线yx3在点(1,1)处的切线与x轴、直线x2 所围成的三角形的面积为 _。 9、 函数的单调性 函数 y)(xf在某个区间内可导,若)(xf 0,则)(xf为 ; 若)(xf 0,则)(xf为 .(2) 如果在某个区间内恒有0)( xf,则)(xf .10、已知曲线 y=.34 313x(1)求曲线在 x=2 处的切线方程; (2)求曲线过点(2,4)的切线方程.11、已知函数 f(x)=x3+ax
3、2+bx+c,曲线 y=f(x)在点 x=1 处的切线为 l:3x-y+1=0,若 x=时,y=f(x)有极值.32(1)求 a,b,c 的值; (2)求 y=f(x)在-3,1上的最大值和最小值.12、已知 f(x)=ex-ax-1. (1)求 f(x)的单调增区间; (2)若 f(x)在定义域 R R 内单调递增,求 a 的取值范围; (3)是否存在 a,使 f(x)在(-,0上单调递减,在0,+)上单调递增? 若存在,求出 a 的值;若不存在,说明理由.13、某造船公司年造船量是 20 艘,已知造船 x 艘的产值函数为 R(x)=3 700x+45x2-10x3(单位:万元),成本函数为
4、 C(x)=460x+5 000(单位:万元), 又在经济学中,函数 f(x)的边际函数 Mf(x)定义为 Mf(x)=f(x+1)-f(x). (1)求利润函数 P(x)及边际利润函数 MP(x);(提示:利润=产值-成本) (2)问年造船量安排多少艘时,可使公司造船的年利润最大? (3)求边际利润函数 MP(x)的单调递减区间,并说明单调递减在本题中的实际 意义是什么?内部资料,请勿外传!#XuyUP2kNXpRWXmA&UE9aQGn8xp$R#͑GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!
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