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: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)=

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) =

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

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 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(x) be a continuous & differentiable function on R satisfying f(-x)=f(x)&f(3+x)=f(3-x)AA x in R . If f'(1)=-5 then f'(7) =

If f is a real- valued differentiable function satisfying |f(x) - f(y)| le (x-y)^(2) ,x ,y , in R and f(0) =0 then f(1) equals

Let f : R rarr R be a differentiable function satisfying f(x) = f(y) f(x - y), AA x, y in R and f'(0) = int_(0)^(4) {2x}dx , where {.} denotes the fractional part function and f'(-3) - alpha e^(beta) . Then, |alpha + beta| is equal to.......