Let f be a function so that (below). Which must be true? I. f is continuous at x=2 II. f is differentiable at x=2 III. The derivative of f is continuous at x=2 (A) I (B) II (C) I & II (D) I & III (E) II & III
Noting that a function
the given information effectively is that
Now, looking at the statements:
Differentiability of a function at a point implies its continuity at that point.
The given information matches the definition of differentiability at
The derivative of a function is not necessarily continuous, a classic example being