If f x = x f o r ≤ 0 0 f o r 0 then f ( x ) at x = 0 is

Question

If f x = x f o r ≤ 0 0 f o r > 0 then f ( x ) at x = 0 is, Continuous but not differentiable, Not continuous but differentiable, Continuous and differentiable, Not continuous and not differentiable

MARKS App · Accepted Answer

Continuity at x = 0 lim x → 0 - ⁡ f x = lim x → 0 ⁡ x = 0 lim x → 0 + ⁡ f x = 0 f ( 0 ) = 0 ∴ c o n t i n u o u s a t x = 0 For differentiability f ' ( 0 + ) = 0 f ' ( 0 − ) = 1 ∴ Not differentiable Alternative Diagram: It has sharp edge at x = 0 ∴ not differentiable but continuous

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