If a curve `y=f(x)` satisfies `y''x^2+x(y')^2=2x y',f(0)=0 and f'(1)=1,` then f(x) is

If a curve y=f(x) satisfies y''x^(2)+x(y')^(2)=2xy',f(0)=0 and f'(1)=1 then f(x) is

If y=f(x) satisfies f(x+1)+f(z-1)=f(x+z) AA x, z in R and f(0)=0 and f'(0)=4 then f(2) is equal to

A function y=f(x) satisfying f'(x)=x^(-(3)/(2)),f'(4)=2 and f(0)=0 is

If f((x)/(y))=(f(x))/(f(y)),AA y,f(y)!=0 and f'(1)=2, find f(x)

The curve y =f (x) satisfies (d^(2) y)/(dx ^(2))=6x-4 and f (x) has a local minimum vlaue 5 when x=1. Then f^(prime)(0) is equal to :

A function y=f(x) satisfies f''(x)=-(1)/(x^(2))-pi^(2)sin(pi x)f'(2)=pi+(1)/(2) and f(1)=0 then value of f((1)/(2)) is

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

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