Find the local extrema then classify them

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SUMMARY

The discussion focuses on the mathematical process of finding and classifying local extrema in functions, emphasizing the importance of identifying turning points. Participants debate whether to include detailed explanations or to present strictly mathematical solutions. The consensus leans towards maintaining essential mathematical steps while minimizing conversational content. Key steps include determining turning points and classifying them based on their nature.

PREREQUISITES
  • Understanding of calculus concepts, specifically derivatives
  • Familiarity with the definition of local extrema
  • Knowledge of classification methods for turning points
  • Proficiency in mathematical notation and problem-solving
NEXT STEPS
  • Study the process of finding derivatives to locate turning points
  • Learn techniques for classifying local extrema using the second derivative test
  • Explore graphical methods for visualizing local extrema in functions
  • Practice solving problems involving local extrema in calculus textbooks
USEFUL FOR

Students studying calculus, educators teaching mathematical concepts, and anyone interested in understanding the classification of local extrema in functions.

ttpp1124
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Homework Statement
For the function ##f(x) = 3 +5x^2-2x^5##, find the local extrema. Then, classify the local extrema (maximum or minimum points) using the second derivative test.
Relevant Equations
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So this is a very long answer for a question worth 4 marks. Would it be a good idea to keep the explanation, or to have it strictly math only?
 
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ttpp1124 said:
So this is a very long answer for a question worth 4 marks. Would it be a good idea to keep the explanation, or to have it strictly math only?

How would you have answered the question differently, I wonder? You wouldn't need to write those last three bullet points, nor particularly any of the conversational text between the equations, but the key mathematical steps must be finding the turning points and classifying the turning points.
 
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etotheipi said:
How would you have answered the question differently? You wouldn't need to write those last three bullet points, nor particularly any of the conversational text between the equations, but the key mathematical steps must be finding the turning points and classifying the turning points.
Thank you for the suggestion
 

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