please help me solve. ### Finding Relative ExtremaTo determine the relative extrema of the function and classify each as a maximum or minimum, follow these instructions. (You may use either the first or second derivative test.)Given function:\[ f(x) = x^3 - 12x - 4 \]1. **Find the first derivative, $ f'(x) $**: Differentiate the function with respect to $ x $ to find the first derivative.2. **Find critical points**: Set the first derivative equal to zero and solve for $ x $: $ f'(x) = 0 $.3. **Classify the critical points**: Utilize either the first derivative test or the second derivative test: - **First Derivative Test**: Analyze the sign changes of $ f'(x) $ around the critical points. - **Second Derivative Test**: Find the second derivative $ f''(x) $. Determine the concavity at each critical point by evaluating $ f''(x) $.Make sure to classify the extrema appropriately as either a maximum or minimum based on the results of these tests.

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Description: please help me solve. ### Finding Relative ExtremaTo determine the relative extrema of the function and classify each as a maximum or minimum, follow these instructions. (You may use either the first or second derivative test.)Given function:\[ f(x)

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Find the relative extrema of the function and classify each as a maximum or minimum. (Use either the first or second derivative test). f(x) = x 3 - 12x - 4

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Statistics is the study of data collection, organization, analysis, interpretation, and presentation. Statistical bias is a characteristic of a statistical technique or its findings in which the expected value deviates from the actual root quantitative parameter being estimated. According to the actual definition of bias, it refers to the tendency of a statistic to overestimate or underestimate a parameter.

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please help me solve.

### Finding Relative Extrema

To determine the relative extrema of the function and classify each as a maximum or minimum, follow these instructions. (You may use either the first or second derivative test.)

Given function:
\[ f(x) = x^3 - 12x - 4 \]

1. **Find the first derivative, $ f'(x) $**:
Differentiate the function with respect to $ x $ to find the first derivative.

2. **Find critical points**:
Set the first derivative equal to zero and solve for $ x $:
$ f'(x) = 0 $.

3. **Classify the critical points**:
Utilize either the first derivative test or the second derivative test:
- **First Derivative Test**: Analyze the sign changes of $ f'(x) $ around the critical points.
- **Second Derivative Test**: Find the second derivative $ f''(x) $. Determine the concavity at each critical point by evaluating $ f''(x) $.

Make sure to classify the extrema appropriately as either a maximum or minimum based on the results of these tests.

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