MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation
Problem
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.