Suppose that `f(0)=-3` and `f'(x)<=5` for all real values of `x`. Then the largest value of `f(2)` can attain is

Suppose that f(0)=0 and f'(0)=2, and g(x)=f(-x+f(f(x))). The value of g'(0) is equal to -

Let f (x + y) = f(x) f(y) for all x, y, in R , suppose that f(3) = 3 and f '(0) = 2 then f '(3) is equal to-

Let F:RtoR be a thrice differntiable function. Suppose that F(1)=0,F(3)=-4 and F'(x)lt0 for all x epsilon(1//2,3) . Let f(x)=xF(x) for all x inR . Then the correct statement(s) is (are)

Let F : R to R be a thrice differentiable function . Suppose that F(1)=0,F(3)=-4 and F(x) lt 0 for all x in (1,3) . f(x) = x F(x) for all x inR . If int_(1)^(3)x^(2)F'(x)dx=-12 andint_(1)^(3)x^(3)F'' (x)dx =40 , then the correct expression (s) is //are

Suppose that f(0)=0a n df^(prime)(0)=2, and let g(x)=f(-x+f(f(x)))dot The value of g' (0) is equal to _____

Suppose that f(x)f(f(x))=1 and f(1000)=999 then which of the following is true

Let f(x + y) = f(x) .f(y) AA x, y in R suppose that f(k) =3, k in R and f'(0) = 11 then find f'(k)

Suppose that g(x)=1+sqrt(x) and f(g(x))=3+2sqrt(x)+xdot Then find the function f(x)dot

Let f(x)=ax^(2)+bx+c , a ne 0 , a , b , c in I . Suppose that f(1)=0 , 50 lt f(7) lt 60 and 70 lt f(8) lt 80 . Number of integral values of x for which f(x) lt 0 is

A function f: R->R satisfies that equation f(x+y)=f(x)f(y) for all x ,\ y in R , f(x)!=0 . Suppose that the function f(x) is differentiable at x=0 and f^(prime)(0)=2 . Prove that f^(prime)(x)=2\ f(x) .