Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
Bartleby Related Questions Icon

Related questions

bartleby

Concept explainers

Topic Video
Question

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.
expand button
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.
Expert Solution
Check Mark
Knowledge Booster
Background pattern image
Calculus
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Text book image
Calculus: Early Transcendentals
Calculus
ISBN:9781285741550
Author:James Stewart
Publisher:Cengage Learning
Text book image
Thomas' Calculus (14th Edition)
Calculus
ISBN:9780134438986
Author:Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:PEARSON
Text book image
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:9780134763644
Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:PEARSON
Text book image
Calculus: Early Transcendentals
Calculus
ISBN:9781319050740
Author:Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:W. H. Freeman
Text book image
Precalculus
Calculus
ISBN:9780135189405
Author:Michael Sullivan
Publisher:PEARSON
Text book image
Calculus: Early Transcendental Functions
Calculus
ISBN:9781337552516
Author:Ron Larson, Bruce H. Edwards
Publisher:Cengage Learning