Answer: dy/dx = (dy/dt) divided by (dx/dt).
- A dy/dx = dx/dt divided by dy/dt
- B dy/dx = (dy/dt) divided by (dx/dt)
- C dy/dx = dy/dt times dx/dt
- D dy/dx = dt/dy
Correct answer: B. dy/dx = (dy/dt) divided by (dx/dt)
Explanation: For parametric curves, dy/dx = (dy/dt) / (dx/dt), provided dx/dt is not zero.
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.