函数y=x2(x>0)的图象在点(ak,ak2)处的切线与x轴交点的横坐标为ak+1,k为正整数,a1=16,则a1+a3+a5=(  ) A.18 B.21 C.24 D.30

问题描述:

函数y=x2(x>0)的图象在点(ak,ak2)处的切线与x轴交点的横坐标为ak+1,k为正整数,a1=16,则a1+a3+a5=(  )
A. 18
B. 21
C. 24
D. 30

依题意,y′=2x,
∴函数y=x2(x>0)的图象在点(ak,ak2)处的切线方程为y-ak2=2ak(x-ak
令y=0,可得x=

1
2
ak,即ak+1=
1
2
ak
∴数列{an}为等比数列an=16×(
1
2
n-1
∴a1+a3+a5=16+4+1=21
故选B