How to solve
For a smooth curve, a horizontal tangent has f'(x) = 0 and marks a critical number. A turning point can be a local maximum or minimum.
Steps
- Find the turning point with a horizontal tangent.
- Read its x-coordinate.
- Use the opening direction to classify it as a maximum or minimum.
Example
An upward-opening parabola has vertex (2, −1).
- The tangent is horizontal at x = 2.
- The graph turns upward, so it is a local minimum.
Answer: 2
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