If `f(0)=0,f^(prime)(0)=2,` then the derivative of `y=f(f(f(x)))` at `x=0` is 2 (b) 8 (c) 16 (d) 4

If f(x + y) = f(x) +f(y), then the value of f(0)

If f(0) = 0 ,f'(0) = 2 , then the value differentiable at x = 0 of function y = f[f{f(x)}] is _

If y=f{f(x)} , f(0) =0 and f'(0)=5, then the value of [(dy)/(dx)]_(x=0) is-

Consider the function f(x)={xsinpi/x ,forx >0 ,forx=0 The number of point in (0,1) where the derivative f^(prime)(x) vanishes is (a) 0 (b) 1 (c) 2 (d) infinite

Let f: R->R be a continuous function and f(x)=f(2x) is true AAx in Rdot If f(1)=3, then the value of int_(-1)^1f(f(x))dx is equal to (a)6 (b) 0 (c) 3f(3) (d) 2f(0)

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 _____

Let f RR rarr RR be differentiable at x = 0 . If f(0) = 0 and f'(0) = 2, then the value of underset(x rarr 0)lim (1)/(x)[f(x) + f(2x) + f(3x)+…+f(2015x)] is

If f(x) = x+ 1/x , x>0 then the greatest value of f(x) is (a) -2 (b)0 (c) 3 (d) none of these

Let f be a function with continuous second derivative and f(0)=f^(prime)(0)=0. Determine a function g by g(x)={(f(x))/x ,x!=0; 0,x=0 Then which of the following statements is correct? a. g has a continuous first derivative b. g has a first derivative c. g is continuous but g fails to have a derivative d. g has a first derivative but the first derivative is not continuous

Let f (x) be a differentiable function and f '(1) =4,f'(2) =6 where f '(c ) means the derivative of function f(x) at x=c. Then lim _(hto0)(f(2 +2h +h^(2))-f(2))/(f (1+h-h^(2))-f(1)) is equal to-