Let `f` be a differentiable function satisfying `f(x+2y)=2yf(x)+xf(y)-3xy+1` `AA x , y` in `R` such that `f'(0)=1` ,then value of `f(8)` is equal

Let f:R rarr R be a differentiable function satisfying 2f((x+y)/(2))-f(y)=f(x) AA x , y in R ,if f(0)=5 and f'(0)=-1 , then f(1)+f(2)+f(3) equals

Let f(x) be a differentiable function satisfying f(y)f((x)/(y))=f(x)AA,x,y in R,y!=0 and f(1)!=0,f'(1)=3 then

Let f:R rarr R be a differential function satisfy f(x)=f(x-y)f(y)AA x,y in R and f'(0)=a,f'(2)=b then f'(-2)=

Let f be a real valued differentiable function satisfying f(x+y)=f(x)+f(y)-xy-1,AA x,y in R and f(1)=1. Equation ofthe normal to the graph of f(x) at the point where y=f(x) cuts the y-axis,is

If f:R rarr R be a differentiable function such that f(x+2y)=f(x)+f(2y)+4xy, AA x,y in R , f(2)=10 , then f(3)=?

Let f be a differentiable function satisfying the relation f(xy)=xf(y)+yf(x)-2xy (where x,y>0) and f'(1)=3, then

Let f be a real valued function, satisfying f (x+y) =f (x) f (y) for all a,y in R Such that, f (1_ =a. Then , f (x) =

If f is a differentiable function satisfying 2f(x)=f(xy)+f((x)/(y)),AA x,y in R^(+), f(1)=0 and f'(1)=(1)/(ln6), then f(7776) =