A) decreasing on (0, 2)
B) decreasing on (0, 1) and increasing on (1, 2)
C) increasing on (0, 2)
D) increasing on (0, 1) and decreasing on (1, 2)
Correct Answer: B
Solution :
\[\phi (x)=f(x)+f(2-x)\] \[\phi '(x)=f'(x)-f'(2-x)\] ...... Since \[f''(x)>0\] \[\Rightarrow \]\[f'(x)\] is increasing \[\forall x\in (0,2)\] Case-I : When \[x>2-x\Rightarrow x>1\] \[\Rightarrow \]\[\phi '(x)>0\forall x\in (1,2)\] \[\therefore \]\[\phi (x)\] is increasing on (1, 2) Case-II :When \[x<2-x\Rightarrow x<1\] \[\phi '(x)<0\forall x\in (0,1)\] \[\therefore \]\[\phi (x)\] is decreasing on (0, 1)You need to login to perform this action.
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