设函数f(x)=(a/3)x^3+bx^2+cx+d的图像关于原点对称,f'(a)=0且f(x)在点P(1,m)处的切线与直线x-6y+2=0垂直,求f(x)的解析式.

问题描述:

设函数f(x)=(a/3)x^3+bx^2+cx+d的图像关于原点对称,f'(a)=0且f(x)在点P(1,m)处的切线与直线x-6y+2=0垂直,求f(x)的解析式.

(a/3)x³+cx,
f′(x)=ax²+c,a³+c=0
a+c=-6
a³-a-6=0
a=2,
c=-8
f(x)=(2/3)a³-8x