Question

Let f(x) satisty the requirement of Lagrange's mean value theorem in [0, 2]. If f(0) = 0  and |f '(x)| ≤ 1 2 for all x ∈[0, 2], then

(A) f(x) ≤ 2 

(B) |f(x)| ≤ 1 

(C) |f(x)| ≤ |x| 

(D) f(x) = 3 for at least one x in [0, 2]

Answer 1

Correct Option :- (B) (C)

Explanation :-