Let f(x) satisfy the requirements of Lar...

Let f(x) satisfy the requirements of Largrange's Mean Value Theorem in [0, 2]. If f(0) = 0 and `|f'(x)| le (1)/(2)`, for all x in [0, 2], then :

A

`f(x)le2`

B

`|f(x)|le2x`

C

`|f(x)|le1`

D

`f(x)=3`

Verified by Experts

Similar Questions

Explore conceptually related problems

Let f be differentiable for all x. If f(1)= -2, f'(x) ge 2 for all x in [1, 6] , then :

Let f(x) = e^(x), x in [0,1] , then a number c of the Lagrange's mean value theorem is

If f(x) satisfiles requirements of Rolle's theorem in [1,2] and f(x) is continuous in [1,2], then int_1^2 f'(x) dx is :

If f(x) satisfies the conditions of Rolle's Theorem on [1,2] , then int_1^2 f'(x) dx equals:

If 2f(x) = f^(')(x) and f(0) = 3, then f(2) =

There exists a function f(x) satisfying f(0)=1, f'(0)=-1, f(x) gt 0 , for all x, then :

The value of c in Mean value theorem, for the function f(x) = x(x2) and x in [1,2] is

If f(pi) = 2 and int_0^(pi) [f(x)+f^('')(x)] sin x dx = 5 then f(0)

Let f(x+(1)/(x))=x^(2)+(1)/(x^(2)), x ne 0, then f(x)=