Maths doubt

[The Villain]

Let g(x)=f(x)+f(1-x) and f"(x)>0 for all x belongs to(0,1) then g(x) is

a increasing on (0,1/2) and decreasing on (1/2,1)
b increasing on (1/2,1) and decreasing on (0,1/2)
c increasing on (0,1)
d decreasing on (0,1

[Sinistral]

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[The Villain]

Thanxxx

[Noel]

@sinistral..please forgive me for pointing out but is it not incorrect to say that f ''(x)>0 implies that f is increasing..in the proof stated above?

[SINGHAM]

He has never said so! He has said that f''(x)>0 implies that f'(x) that is the derivative of f is increasing. But that does not imply that f is increasing, too. Think e.g.f(x)=(1/2)x^2 ,so f'(x)=x, where f'(x)<0 for x<0 and so f is decreasing there. But, still, f''(x)=1>0. Thus, f'' determines curvature, that is , affects f indirectly, and f' directly.

[Noel]

Ya i got it.my bad.thanks :)