If f(x) is continuous and differerntiable function such that `f((1)/(n))=0` for all `n in N`, then

If f(x) is a continuous and differentiable function and f((1)/(n))=0AA n>=I and n in I, then a) f(x)=0,x in(0,1] b) f(c)=0,f(0)=0 c),(0)=0=f(0),x in(0,1] d) f(0)=0 and f'(0) need not be zero

Let f:NrarrN in such that f(n+1)gtf(f(n)) for all n in N then

If f is continuous and differentiable function and f(0)=1,f(1)=2, then prove that there exists at least one c in[0,1] for which f'(c)(f(c))^(n-1)>sqrt(2^(n-1)), where n in N.

A function f:R to R is differernitable and satisfies the equation f((1)/(n)) =0 for all integers n ge 1 , then

If f(x) is a real-valued function discontinuous at all integral points lying in [0,n] and if (f(x))^(2)=1, forall x in [0,n], then number of functions f(x) are

Let f(x) be a continuous function such that int_(n)^(n+1) f(x) dx=n^(3) , ninZ . Then the value of the integeral int_(-3)^(3) f(x) dx, is

If f(x) is a real valued functions satisfying f(x+y) = f(x) +f(y) -yx -1 for all x, y in R such that f(1)=1 then the number of solutions of f(n) = n,n in N , is

Let f : N rarr N be defined as f(x) = 2x for all x in N , then f is

The function f(x)=|cos sx| is everywhere continuous and differentiable everywhere continuous but not differentiable at (2n+1)(pi)/(2),n in Z .neither continuous not differentiable at (2x+1)(pi)/(2),n in Z