Project ForgeEngineering Mathematics
Calculus
GATE 2012
Easy
Consider the function f(x)=|x| in the interval −1≤x≤1. At the point x=0, f(x) is
- Acontinuous and differentiable.
- Bnon-continuous and differentiable.
- continuous and non-differentiable.
- Dneither continuous nor differentiable.
Explanation
f(x)=|x| is continuous everywhere, including x=0 (no jump). But its derivative from the left is −1 and from the right is +1 at x=0 — the one-sided derivatives disagree, so f is NOT differentiable at x=0. Hence continuous but non-differentiable.
Source: GATE ME 2012 (Booklet Code A) (2012)
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