Answer: Zero (first derivative test).
- A Positive, since the function is still increasing
- B Negative, since the function has started decreasing
- C Zero (first derivative test)
- D Undefined, since the slope cannot be computed there
Correct answer: C. Zero (first derivative test)
Explanation: At a maximum or minimum, f'(x) = 0 (critical point). Check sign of f'' to distinguish.
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