Let f be the function defined by f(x)=∣x∣ for all real numbers x.
Throughout this problem, you may assume standard limit properties but must provide complete justification for any statements about continuity or differentiability.
(1) Demonstrate that f is continuous at x=0.
(2) Compute the difference–quotient limits that define the left–hand and right–hand derivatives of f at x=0. State each one explicitly.
(3) Using your results from part (b), determine whether f is differentiable at x=0 and justify your conclusion.