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Local extrema

from class:

Algebra and Trigonometry

Definition

Local extrema are points on a graph where the function reaches a local maximum or minimum within a given interval. These points are identified by analyzing the first derivative of the function.

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5 Must Know Facts For Your Next Test

  1. A local maximum is a point where the function changes direction from increasing to decreasing.
  2. A local minimum is a point where the function changes direction from decreasing to increasing.
  3. Local extrema occur where the first derivative of the function is zero or undefined.
  4. The second derivative test can help determine whether a critical point is a local maximum, local minimum, or neither.
  5. Local extrema are important in understanding the overall shape and behavior of a graph.

Review Questions

  • What is the difference between a local maximum and a local minimum?
  • How do you find potential local extrema using the first derivative?
  • What role does the second derivative play in identifying local extrema?
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