Let `g(x)=f(x)+f(1-x)` and `f''(x)<0`, `0<=x<=1`. Then

Let g(x)=2f((x)/(2))+f(1-x) and f'(x)<0 in 0<=x<=1 then g(x)

Let g(x)=2f(x/2)+f(1-x) and f^(primeprime)(x)<0 in 0<=x<=1 then g(x)

Let f(x+y)=f(x) f(y) and f(x)=1+(sin 2x)g(x) where g(x) is continuous. Then, f'(x) equals

Let f(x+y)=f(x)f(y) and f(x) = 1 + (sin2x) g(x) where g(x) is continuous . Then f^(1) (x) equals

Let f(x+y)=f(x)f(y) and f(x)=1+(sin2x)g(x) , where g(x) is continuous. Then f'(x) is equal to :

Let g(x)=e^(f(x)) and f(x+1)=x+f(x) AA x in R . If n in I^(+)", then"(g'(n+(1)/(2)))/(g(n+(1)/(2)))-(g'((1)/(2)))/(g((1)/(2)))=

Let f(x) be a function such that f(x), f'(x) and f''(x) are in G.P., then function f(x) is

Let f(x) be a function such that f(x), f'(x) and f''(x) are in G.P., then function f(x) is

Let f (x)=(x+1) (x+2) (x+3)…..(x+100) and g (x) =f (x) f''(x) -f ('(x)) ^(2). Let n be the numbers of rreal roots of g(x) =0, then: