1.已知曲线C:y=4ax^3+x,过点Q(0,-1)做曲线C的切线l,切点为P.(1)求证:不论a取何值,切点P总在一定直线上.(2)若a>0,设曲线在P点的切线的垂线与x轴交于T,求|OT|的最小值.2.设f(x)为可导函数,且满足limf(1)-
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![1.已知曲线C:y=4ax^3+x,过点Q(0,-1)做曲线C的切线l,切点为P.(1)求证:不论a取何值,切点P总在一定直线上.(2)若a>0,设曲线在P点的切线的垂线与x轴交于T,求|OT|的最小值.2.设f(x)为可导函数,且满足limf(1)-](/uploads/image/z/3893851-19-1.jpg?t=1.%E5%B7%B2%E7%9F%A5%E6%9B%B2%E7%BA%BFC%3Ay%3D4ax%5E3%2Bx%2C%E8%BF%87%E7%82%B9Q%280%2C-1%29%E5%81%9A%E6%9B%B2%E7%BA%BFC%E7%9A%84%E5%88%87%E7%BA%BFl%2C%E5%88%87%E7%82%B9%E4%B8%BAP.%281%29%E6%B1%82%E8%AF%81%3A%E4%B8%8D%E8%AE%BAa%E5%8F%96%E4%BD%95%E5%80%BC%2C%E5%88%87%E7%82%B9P%E6%80%BB%E5%9C%A8%E4%B8%80%E5%AE%9A%E7%9B%B4%E7%BA%BF%E4%B8%8A.%282%29%E8%8B%A5a%EF%BC%9E0%2C%E8%AE%BE%E6%9B%B2%E7%BA%BF%E5%9C%A8P%E7%82%B9%E7%9A%84%E5%88%87%E7%BA%BF%E7%9A%84%E5%9E%82%E7%BA%BF%E4%B8%8Ex%E8%BD%B4%E4%BA%A4%E4%BA%8ET%2C%E6%B1%82%7COT%7C%E7%9A%84%E6%9C%80%E5%B0%8F%E5%80%BC.2.%E8%AE%BEf%28x%29%E4%B8%BA%E5%8F%AF%E5%AF%BC%E5%87%BD%E6%95%B0%2C%E4%B8%94%E6%BB%A1%E8%B6%B3limf%281%29-)
1.已知曲线C:y=4ax^3+x,过点Q(0,-1)做曲线C的切线l,切点为P.(1)求证:不论a取何值,切点P总在一定直线上.(2)若a>0,设曲线在P点的切线的垂线与x轴交于T,求|OT|的最小值.2.设f(x)为可导函数,且满足limf(1)-
1.已知曲线C:y=4ax^3+x,过点Q(0,-1)做曲线C的切线l,切点为P.(1)求证:不论a取何值,切点P总在一定直线上.(2)若a>0,设曲线在P点的切线的垂线与x轴交于T,求|OT|的最小值.2.设f(x)为可导函数,且满足limf(1)-f(1-2x)/x ,x→0.则过f(x)上点(1,f(1))处的切线斜率是多少?3.在正项等差数列{an}和正项等比数列{bn}中,已知常数m,n,k,t属于正整数,且t<k,若am=bn,a(m+k)=b(n+k),则a(m+t)/b(n+t)的范围是( )A.(1,正无穷) B.(1/2,1] C.[1,正无穷) D.(0,
1.已知曲线C:y=4ax^3+x,过点Q(0,-1)做曲线C的切线l,切点为P.(1)求证:不论a取何值,切点P总在一定直线上.(2)若a>0,设曲线在P点的切线的垂线与x轴交于T,求|OT|的最小值.2.设f(x)为可导函数,且满足limf(1)-
.哎呀...哎呀...我脑壳痛.
马上 (1)令y'=12ax+1 设P(x0,y0) 设kPQ=(y0-1)/x0 又因为k=12ax0+1 所以(y0-1)/x0=12ax0+1 ==>12ax0+x0=y0-1 ==>12ax0+x0=4ax0+x0-1 ==>x0=1/2√a ① 再代入y=4ax+x ==>y0=1/2+1/2√a② 由②-①可得y0-x0=1/2 ==>x0-y0+1/2=0 所以P总在直线L上