Answer: Strictly decreasing.
- A Strictly increasing
- B Constant
- C Strictly decreasing
- D Has a maximum
Correct answer: C. Strictly decreasing
Explanation: A negative derivative throughout an interval means the function is strictly decreasing on that interval.
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.