y=f(x), where f satisfies the relation `f(x+y)=2f(x)+xf(y)+ysqrt(f(x))`,`AAx,y->R` and f'(0)=0.Then f(6)is equal ______

If f satisfies the relation f(x+y)+f(x-y)=2f(x)f(y)AA x,y in K and f(0)!=0; then f(10)-f(-10)-

If the function / satisfies the relation f(x+y)+f(x-y)=2f(x),f(y)AA x,y in R and f(0)!=0 ,then f(x) is an even function f(x) is an odd function If f(2)=a, then f(-2)=a If f(4)=b, then f(-4)=-b

A function f(x) satisfies the relation f(x+y) = f(x) + f(y) + xy(x+y), AA x, y in R . If f'(0) = - 1, then

Let f(x+y) + f(x-y) = 2f(x)f(y) for x, y in R and f(0) != 0 . Then f(x) must be

If f(x+y) = f(x) + f(y) + |x|y+xy^(2),AA x, y in R and f'(0) = 0 , then

Find function f(x) which is differentiable and satisfy the relation f(x+y)=f(x)+f(y)+(e^(x)-1)(e^(y)-1)AA x, y in R, and f'(0)=2.