Question

determine whether the statement is true or false. if it is false, give an example that shows it is false. if a function is continuous at a point, then it is differentiable at that point. true. false. f(x) = |x - 2| is continuous, but not differentiable at x = 2. false. f(x) = 1/x is continuous, but not differentiable at x = 1. false. f(x) = x^2 is continuous, but not differentiable at x = 0. false. f(x) = x^3 is continuous, but not differentiable at x = 0. resources read it

Explanation:

Continuity does not imply differentiability. A continuous function may lack a derivative at points with corners or cusps.

Answer:

B. False. f(x) = |x - 2| is continuous, but not differentiable at x = 2.