Answer: Local minimum.
- A Local maximum
- B Local minimum
- C Point of inflection
- D Discontinuity
Correct answer: B. Local minimum
Explanation: A positive second derivative at a critical point indicates the curve is concave up there, giving a local minimum.
The tangent at a point touches the curve with slope f'(a); the normal is the line perpendicular to the tangent at that same point, with slope -1/f'(a) - together they describe the curve's local direction and the line "straight into" the curve.
Concept context
Use derivatives to study rate of change, increasing and decreasing functions, tangents and normals, and maxima and minima, with classic optimization problems.