Answer: the negative reciprocal.
- A the negative reciprocal
- B exactly the same value
- C twice as large a value
- D the square of it
Correct answer: A. the negative reciprocal
Explanation: The normal is perpendicular to the tangent, so its slope is the negative reciprocal.
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.