determine whether the statement is true or false. if it is false, give an example that shows it is false. if…

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

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

Answer

Brief Explanations:

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.