If f (x) = |3 − x| + (3 + x), where (x) denotes the least integer greater than or equal to x, then f (x) is

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(d) neither differentiable nor continuous at x = 3 We have, f\left( x ight) = \left| 3 - x ight| + \left( 3 + x ight), 	ext { where } \left( x ight) 	ext{denotes the least integer greater than or equal to} x . `f(x) = {(3-x +3+3,2<x<3),(-3 +x + 3 +4,3<x<4):} ⇒ f(x) = {(-x +9,2<x<3),(x+4 , 3<x<4):}` Here, \left( 	ext { LHL at x } = 3 ight) = \lim_{x 	o 3^-} f\left( x ight) = \lim_{x 	o 3^-} \left( - x + 9 ight) = - 3 + 9 = 6 \left( 	ext { RHL at x }= 3 ight) = \lim_{x 	o 3^+} f\left( x ight) = \lim_{x 	o 3^-} \left( x + 4 ight) = 3 + 4 = 7 	ext { Since, } \left( 	ext { LHL at x } = 3 ight) 
eq \left( 	ext { RHL at x }= 3 ight) 	ext{Hence, given function is not continuous at x} = 3 	ext{Therefore, the function will also not be differentiable at} x = 3

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