Answer: instantaneous rate of change.
- A instantaneous rate of change
- B the total enclosed area
- C the average value only
- D the solid volume value
Correct answer: A. instantaneous rate of change
Explanation: The derivative is the instantaneous rate of change (the slope of the tangent).
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.