Answer: -cot(t).
- A tan(t)
- B -tan(t)
- C -cot(t)
- D cot(t)
Correct answer: C. -cot(t)
Explanation: dx/dt = -a sin(t), dy/dt = a cos(t). dy/dx = (a cos t)/(-a sin t) = -cot(t).
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.