Let f : [0, 2] → R be a twice differentiable function such that f ’(x) > 0, for all x 
(0, 2). If 
(x) = f(x) + f(2 − x), then 
is
(a) Decreasing on (0, 2)
(b) Increasing on (0, 2)
(c) Decreasing on (0, 1) and increasing on (1, 2)
(d) Increasing on (0, 1) and decreasing on (1, 2)
(0, 2). If (x) = f(x) + f(2 − x), then isQuestion ID - 57548 | SaraNextGen Top Answer Let f : [0, 2] → R be a twice differentiable function such that f ’(x) > 0, for all x (0, 2). If (x) = f(x) + f(2 − x), then is
(a) Decreasing on (0, 2)
(b) Increasing on (0, 2)
(c) Decreasing on (0, 1) and increasing on (1, 2)
(d) Increasing on (0, 1) and decreasing on (1, 2)
Let f : [0, 2] → R be a twice differentiable function such that f ’(x) > 0, for all x (0, 2). If (x) = f(x) + f(2 − x), then is
(a) Decreasing on (0, 2)
(b) Increasing on (0, 2)
(c) Decreasing on (0, 1) and increasing on (1, 2)
(d) Increasing on (0, 1) and decreasing on (1, 2)
(x) = f(x) + f(2 − x)
differentiating w.r.t. x
’(x) = f ’(x) − f ’(2 − x)
For 
(x) to be increasing 
’(x) > 0
⇒ f ’(x) > f ’(2 − x)
( f ’’(x) > 0 then f ’(x) is an increasing function)
⇒ x > 2 − x
⇒ x > 1
So 
(x) is increasing in (1, 2) and decreasing in (0, 1)