Answer: Local minimum.
- A Local maximum
- B Local minimum
- C Saddle point
- D Global maximum
Correct answer: B. Local minimum
Explanation: Second derivative test: f'(a) = 0 identifies a critical point. f''(a) > 0 means f' is increasing through zero, so f changes from decreasing to increasing at a. Therefore f(a) is a local minimum.
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