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 let g(x)=f(-x+f(f(x))). The value of g'(0) is equal to -

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

Let f(x+y)=f(x)*f(y)AA x,y in R suppose that f(3)=3 and f'(0)=11 then f'(3) is given by

Let a>0 and f be continuous in [-a,a]. Suppose that f'(x) exists and f'(x)<=1 for all x in(-a,a). if f(a)=a and f(-a)=-a show that f(0)=0

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 . The correct statement (s) is / are

Let f(x+y)=f(x)f(y) for all x,y in R suppose that f(3)=3,f(0)!=0 and f'(0)=11, then f'(3) is equal

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 epsilonR . 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 . Ifint_(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(x)f(f(x))=1 and f(1000)=999 then which of the following is true