Answer:
Option A,B,C
Explanation:
According to the given data,
F(x)<0,∀xϵ(1,3)
We have, f(x)= x F(x)
⇒ f′(x)=F(x)+xF′(x) .......(i)
⇒ f′(1)=F(1)+F′(1)<0
[given F(1)=0 and F'(x)<0]
Also, f(2)=2F(2)<0
[using F(x)<0,∀xϵ(1,3) ]
Now, f'(x)=F(x)+x F'(x)<0
[using F(x)<0,∀xϵ(1,3) ]
⇒f′(x)<0