Consider the function, … Statement - 1 : … Statement - 2 : … is continuous in [2, 5], differentiable in (2, 5) and …(2) = …(5)

Option C. …f\left( x \right) = \left| {x - 2} \right| = \left\{ {\matrix{ {x - 2\,\,\,,} & {x - 2 \ge 0} \cr {2 - x\,\,\,,} & {x - 2 \le 0} \cr

Limits Continuity and Differentiability

JEE Main 2012 · Annual, Paper 1 · Q4178

MathematicsHard179×since 2002Q4178

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)