# Find the local extrema then classify them

• ttpp1124
In summary, the conversation discusses whether to include a lengthy explanation in a math problem worth 4 marks or to keep it strictly focused on mathematical steps. It is suggested to omit conversational text and focus on finding and classifying turning points as the key mathematical steps.
ttpp1124
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
n/a

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

## 1. What is the definition of a local extrema?

A local extrema is a point on a curve where the value of the function is either at a maximum or minimum compared to the values of the function at surrounding points.

## 2. How do you find the local extrema of a function?

To find the local extrema of a function, you must first take the derivative of the function and set it equal to zero. Then, solve for the variable to find the critical points. Finally, plug in the critical points into the original function to determine if they are a maximum or minimum.

## 3. What is the difference between a local extrema and a global extrema?

A local extrema is a point on a curve where the function is at a maximum or minimum compared to the values of the function at surrounding points. A global extrema is the absolute maximum or minimum value of a function over its entire domain. A local extrema can be a global extrema, but a global extrema is not always a local extrema.

## 4. How do you classify a local extrema?

A local extrema can be classified as a maximum or minimum based on the behavior of the function at that point. If the function is increasing before the critical point and decreasing after, it is a local maximum. If the function is decreasing before the critical point and increasing after, it is a local minimum.

## 5. Why is it important to find the local extrema of a function?

Finding the local extrema of a function is important because it helps us understand the behavior of the function and identify important points on the curve. It also allows us to determine the maximum and minimum values of the function, which can be useful in various applications such as optimization problems.

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