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Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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I keep getting a half point for this questions can you please.
![**Question:**
Find the critical numbers of the function on the interval. List your answers as a comma-separated list. If an answer does not exist, enter DNE.
\[ g(\theta) = 24\theta - 6 \tan \theta \]
\[ \theta = \frac{\pi}{3}, \frac{5\pi}{3}, \frac{2\pi}{3}, \frac{4\pi}{3} \]
**Explanation:**
This question is asking to find the critical numbers of the given trigonometric function \( g(\theta) \). Critical numbers are the values of \(\theta\) at which the derivative of the function \( g'(\theta) \) is zero or undefined. These values indicate where the function may have local maxima or minima, or points of inflection.
To find these critical numbers, you would:
1. Take the derivative of the function \( g(\theta) \).
2. Set the derivative equal to zero and solve for \(\theta\).
3. Identify where the derivative is undefined (if applicable).
4. List the \(\theta\) values found as a comma-separated list.
The provided answer choices suggest the critical numbers for the function over a particular interval. The correct critical numbers are indicated where a checkmark is placed beside the option.](https://content.bartleby.com/qna-images/question/a3097eb0-d5ed-46ab-9dbb-d43a926a2b86/b2df5368-231b-4353-8d9d-1a29bcc719ec/yi2m5ka.jpeg)
Transcribed Image Text:**Question:**
Find the critical numbers of the function on the interval. List your answers as a comma-separated list. If an answer does not exist, enter DNE.
\[ g(\theta) = 24\theta - 6 \tan \theta \]
\[ \theta = \frac{\pi}{3}, \frac{5\pi}{3}, \frac{2\pi}{3}, \frac{4\pi}{3} \]
**Explanation:**
This question is asking to find the critical numbers of the given trigonometric function \( g(\theta) \). Critical numbers are the values of \(\theta\) at which the derivative of the function \( g'(\theta) \) is zero or undefined. These values indicate where the function may have local maxima or minima, or points of inflection.
To find these critical numbers, you would:
1. Take the derivative of the function \( g(\theta) \).
2. Set the derivative equal to zero and solve for \(\theta\).
3. Identify where the derivative is undefined (if applicable).
4. List the \(\theta\) values found as a comma-separated list.
The provided answer choices suggest the critical numbers for the function over a particular interval. The correct critical numbers are indicated where a checkmark is placed beside the option.
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