Consider the function, f(x) = | x - 2 | + | x - 5 |,x R Statement - 1: f'(4) = 0 Statement - 2: f is continuous in [2, 5], differentiable in (2, 5) and f (2) = f (5)

(C) Statement - 1 is true, statement - 2 is true; statement - 2 is not a correct explanation for statement - 1

(A) Statement - 1 is false, statement - 2 is true

(B) Statement - 1 is true, statement - 2 is true; statement - 2 is a correct explanation for statement - 1

(D) Statement - 1 is true, statement - 2 is false

Limit, Continuity and Differentiability: JEE Main 2012 Mathematics question

JEE Main 2012 · Annual, Paper 1 · Q4178

JEE Main 2012Annual, Paper 1MathematicsHardLimit, Continuity and Differentiability420× since 2002

Consider the function,

f\left( x \right) = \left| {x - 2} \right| + \left| {x - 5} \right|,x \in R

Statement - 1 :

f'\left( 4 \right) = 0

Statement - 2 :

f

is continuous in [2, 5], differentiable in (2, 5) and

f

(2) =

f

(5)