Let `varphi(x)=f(x)+f(2a-x)` and `f"(x)>0` for all `x in [0,\ a]` . Then, `varphi(x)` (a) increases on `[0,\ a]` (b) decreases on `[0,\ a]` (c) increases on `[-a ,\ 0]` (d) decreases on `[a ,\ 2a]`

Let phi(a)=f(x)+f(2ax) and f'(x)>0 for all x in[0,a]. Then ,phi(x)

Let g(x)=2f(x/2)+f(2-x) and f''(x)<0 , AA x in (0,2) .Then g(x) increasing in

Let f(x)=tan^(-1)(g(x)) , where g(x) is monotonically increasing for 0

If f(x)=2x+cot^(-1)x+log(sqrt(1+x^(2))-x) then f(x)( a)increase in (0,oo)( b)decrease in [0,oo]( c)neither increases nor decreases in [0,oo]( d) increase in (-oo,oo)

Let g(x)=f(x)+f(1-x) and f'(x)>0AA x in(0,1) Find the intervals of increase and decrease of g(x)

Let f(x): [0, 2] to R be a twice differenctiable function such that f''(x) gt 0 , for all x in (0, 2) . If phi (x) = f(x) + f(2-x) , then phi is (A) increasing on (0, 1) and decreasing on (1, 2) (B) decreasing on (0, 2) (C) decreasing on (0, 1) and increasing on (1, 2) (D) increasing on (0, 2)

Let f''(x)gt0 and phi(x)=f(x)+f(2-x),x in(0,2) be a function then the function phi(x) is (A) increasing in (0,1) and decreasing (1,2) (B) decreasing in (0, 1) and increasing (1,2) (C) increasing in (0, 2) (D) decreasing in (0,2)

g(x)=2f((x)/(2))+f(2-x) and f'(x)<0AA x in(0,2) If g(x) increases in (a,b) and decreases in (c,d), then the value of a+b+c+d-(2)/(3) is

Let g(x)=3f((x)/(3))+f(3-x) and f''(x)>0 for all x in(0,3) . If "g" is decreasing in (0,alpha) and increasing in (alpha,3) ,then 8 alpha is :

The function y=sqrt(2x-x^(2))(A) increases in (0,2)(B) increases in (0,1) but decreases in (1,2)(C) Decreases in (0,2) (D) Increases in (1,2) but decreases in (0,1)