Answer: g(a) is not equal to 0.
- A f(a) = 0
- B g(a) = 0
- C g(a) is not equal to 0
- D f(a) is not equal to 0
Correct answer: C. g(a) is not equal to 0
Explanation: The quotient of two continuous functions is continuous wherever the denominator is nonzero.
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.