Answer: 1.
- A 1
- B 0
- C -1
- D 2
Correct answer: A. 1
Explanation: dx/d(theta) = a(1-cos theta), dy/d(theta) = a sin(theta). dy/dx = sin(theta)/(1-cos theta). At theta=pi/2: sin=1, cos=0, so dy/dx = 1/(1-0) = 1.
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.