极小点
更正题目f(a)=g(a)=0
(f(x)*g(x))’=f'(x)g(x)+f(x)g'(x)
(f(a)*g(a))’=f'(a)g(a)+f(a)g'(a)=0极大点或极小点
下面看f'(x)g(x)+f(x)g'(x)在x=a处的导数
(f'(x)g(x)+f(x)g'(x))’=f''(x)g(x)+f'(x)g'(x)+f(x)g'(x)+f'(x)g'(x)
=f''(x)g(x)+2f'(x)g'(x)+f(x)g'(x)
因为f'(a)*g'(a)>0
(f'(a)g(a)+f(a)g'(a))=f''(a)g(a)+2f'(a)g'(a)+f(a)g'(a)=
2f'(a)g'(a)>0
当x比a小一点时(f(x)*g(x))’=f'(x)g(x)+f(x)g'(x)
0
为极小点