The function f(x) = |x| at x = 0 is:
ABoth continuous and differentiable everywhere
BContinuous but NOT differentiable (sharp corner at 0)
CDifferentiable but not continuous in this case
DNeither continuous nor differentiable at this point
Answer & Solution
Correct answer: B. Continuous but NOT differentiable (sharp corner at 0)
|x| is CONTINUOUS at 0 (limit = 0 = f(0)). But NOT differentiable: left-derivative = -1, right-derivative = +1. The graph has a 'kink' at origin. Continuity does NOT imply differentiability.
Related questions
lim(x→∞) (3x² + x + 1) / (5x² + 2) equals:If f(x) = 1/x, then f′(x) is:lim(x→2) (x³ − 8) / (x² − 4) equals:The derivative of f(x) = √x with respect to x is:lim(x→0) (e^x − 1) / x equals:lim(x→0) (tan x) / x equals:d/dx [(x² + 1)(x + 1)] using product rule equals:If f(x) = 3x² + 5x + 7, then f′(x) is: