Answer: 0.
- A 0
- B 1
- C -1
- D Does not exist
Correct answer: A. 0
Explanation: f(x) = x² (x>0), −x² (x<0). Using first-principles: RHD = lim(h→0⁺) h²/h = 0; LHD = lim(h→0⁻) (−h²)/h = 0. Both one-sided derivatives equal 0, so f'(0) = 0.
As point Q slides along the curve toward P, the secant line PQ rotates into the tangent line at P, whose slope is the derivative.
Concept context
Rate of change, differentiation rules, and applications