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3.3 Increasing and Decreasing Functions and the First Derivative Test

3.3 Increasing and Decreasing Functions and the First Derivative Test. What are we doing?. In this section we are going to be using the derivative to classify whether a relative extrema is either a minima or maxima. How did we do this classification before?.

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3.3 Increasing and Decreasing Functions and the First Derivative Test

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  1. 3.3 Increasing and Decreasing Functions and the First Derivative Test

  2. What are we doing? • In this section we are going to be using the derivative to classify whether a relative extrema is either a minima or maxima. • How did we do this classification before?

  3. Increasing and Decreasing Functions English Translation: a function is increasing if, as x moves to the right, its graph moves up, and is decreasing if its graph moves down

  4. Let’s Look at the value of the Derivative • How does this make sense? • Cool proof on page 169

  5. Example 1: Intervals on Which f is increasing or decreasing. How do we know that it is either increasing or decreasing on the whole interval... Why not both?

  6. The steps we followed

  7. Strictly Monotonic?

  8. The First Derivative Test

  9. Example 2: Applying the First Derivative Test

  10. Example 3: Your Turn • Let us practice our factoring

  11. Example 4: Domain caution • X-values that are not in the domain of function must be used with the critical numbers to determine the test intervals What would happen if we didn’t include in interval?

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