Answer: dy/dx = -x/y.
- A dy/dx = x/y
- B dy/dx = -x/y
- C dy/dx = y/x
- D dy/dx = -y/x
Correct answer: B. dy/dx = -x/y
Explanation: Differentiating both sides: 2x + 2y(dy/dx) = 0, so dy/dx = -x/y.
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.