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  1. The function has

Ask by Guzman Riley. in the United States
Jan 22,2025

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Answer

Problem 22:
  • One relative minimum at
  • Two relative maxima at and
Answer: A. one relative minimum and two relative maxima.
Problem 23:
  • Points of inflection at and
Answer: D. ,

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Mind Expander

To determine the relative extrema of the function , we can start by calculating its first derivative, , and setting it to zero to find critical points. Factoring gives us , leading to critical points at . Evaluating the second derivative, , allows us to confirm maximums at and , and a minimum at . So, you have one relative minimum and two relative maxima (Answer B).
To find the points of inflection, we look for where the second derivative changes sign, starting from . Setting it to zero leads to , resulting in and thus and . These points are where the concavity of the graph changes, providing the x-coordinates of the inflection points!

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