If f(x) is continuous and differentiable function `f((1)/(n))=0 AA n le 1 and n in Z.` then prove that `f(0) =0 and f'(0)=0`

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

lf is a differentiable function satisfying f(1/n)=0,AA n>=1,n in I , then

If f(x) is a twice differentiable function such that f(0)=f(1)=f(2)=0 . Then

If f(x) is a differentiable function satisfying |f'(x)|le4AA x in [0, 4] and f(0)=0 , 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]forw h i c hf^(prime)(c)(f(c))^(n-1)>sqrt(2^(n-1)) , where n in Ndot

If f(x) is continuous in [0,2] and f(0)=f(2). Then the equation f(x)=f(x+1) has

If f(x) is continuous on [0,2] , differentiable in (0,2) ,f(0)=2, f(2)=8 and f'(x) le 3 for all x in (0,2) , then find the value of f(1) .

Suppose |(f'(x),f(x)),(f''(x),f'(x))|=0 where f(x) is continuously differentiable function with f'(x)ne0 and satisfies f(0) = 1 and f'(0) = 2 then lim_(xrarr0) (f(x)-1)/(x) is

If f(x) is continuous and differentiable in x in [-7,0] and f'(x) le 2 AA x in [-7,0] , also f(-7)=-3 then range of f(-1)+f(0)

If f(x) = (a-x^n)^(1/n), a > 0 and n in N , then prove that f(f(x)) = x for all x.