Find the local extrema then classify them

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The discussion focuses on the balance between providing detailed explanations and sticking to strictly mathematical content when answering a question about finding and classifying local extrema. Participants debate whether a lengthy explanation is justified for a question worth only four marks. Key mathematical steps emphasized include identifying turning points and their classification. Suggestions are made to streamline the response by omitting unnecessary conversational text while retaining essential calculations. Ultimately, clarity and conciseness in mathematical communication are prioritized.
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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.
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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
 
First, I tried to show that ##f_n## converges uniformly on ##[0,2\pi]##, which is true since ##f_n \rightarrow 0## for ##n \rightarrow \infty## and ##\sigma_n=\mathrm{sup}\left| \frac{\sin\left(\frac{n^2}{n+\frac 15}x\right)}{n^{x^2-3x+3}} \right| \leq \frac{1}{|n^{x^2-3x+3}|} \leq \frac{1}{n^{\frac 34}}\rightarrow 0##. I can't use neither Leibnitz's test nor Abel's test. For Dirichlet's test I would need to show, that ##\sin\left(\frac{n^2}{n+\frac 15}x \right)## has partialy bounded sums...

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