For the function f(x)=∣x∣, which of the following statements about f at x=0 is most accurate?
a) f is continuous at x=0 and differentiable there with f′(0)=0.
b) f is continuous at x=0 but not differentiable there because the tangent line is vertical (slope undefined).
c) f is continuous at x=0 but not differentiable there because the left-hand and right-hand limits of the difference quotient are not equal.
d) f is continuous at x=0 and differentiable there with f′(0)=1.