Answer: 2f(x).
- A f(x)
- B 2f(x)
- C 2x
- D 2
Correct answer: B. 2f(x)
Explanation: Such an f is e<sup>2x</sup>, and f'(x) = 2e<sup>2x</sup> = 2f(x).
f(x)=|x| is perfectly continuous at x=0 (no break, no jump), but the curve has a sharp corner there: approaching from the left gives slope -1 and from the right gives slope +1 - since these one-sided derivatives disagree, the function is not differentiable at that point.
Concept context
When a function has no breaks (continuity) and when it has a well-defined slope (differentiability), plus rules for differentiating implicit, inverse trig, exponential, log, and parametric functions.