**Transcription for Educational Website:** --- **Problem Statement:** Suppose \( f(t) = 6(t - 4)^{-1/2} \). **(a) Find the derivative of \( f \).** \[ f'(t) = -3(t - 4)^{-3/2} \] *The derivative of the function \( f(t) \) is found using the power rule and chain rule of differentiation.* **(b) Find an equation for the tangent line to the graph of \( y = f(t) \) at the point \( (t, y) = (29, 6/5) \).** *Tangent line:* \[ y = -\frac{3}{125} x + \frac{237}{125} \] *This equation represents the tangent line at the specified point. The slope is calculated using the derivative \( f'(t) \), and the equation is found using the point-slope form.* --- **Additional Information:** In the provided answer section, the values for the derivative and tangent line are confirmed through a second attempt, indicated as "Attempt 2 of 2". *Note: There was an alert symbol (⚠) next to the equation of the tangent line, possibly indicating an error or a point of caution in a digital platform, which should be checked for accuracy.*

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...
icon
Related questions
icon
Concept explainers
Topic Video
Question

I can't figure out the second portion of this question highlighted in red. Can you help me find the equation of the tangent line please? 

**Transcription for Educational Website:**

---

**Problem Statement:**

Suppose \( f(t) = 6(t - 4)^{-1/2} \).

**(a) Find the derivative of \( f \).**

\[ f'(t) = -3(t - 4)^{-3/2} \]

*The derivative of the function \( f(t) \) is found using the power rule and chain rule of differentiation.*

**(b) Find an equation for the tangent line to the graph of \( y = f(t) \) at the point \( (t, y) = (29, 6/5) \).**

*Tangent line:*

\[ y = -\frac{3}{125} x + \frac{237}{125} \]

*This equation represents the tangent line at the specified point. The slope is calculated using the derivative \( f'(t) \), and the equation is found using the point-slope form.*

---

**Additional Information:**

In the provided answer section, the values for the derivative and tangent line are confirmed through a second attempt, indicated as "Attempt 2 of 2". 

*Note: There was an alert symbol (⚠) next to the equation of the tangent line, possibly indicating an error or a point of caution in a digital platform, which should be checked for accuracy.*
Transcribed Image Text:**Transcription for Educational Website:** --- **Problem Statement:** Suppose \( f(t) = 6(t - 4)^{-1/2} \). **(a) Find the derivative of \( f \).** \[ f'(t) = -3(t - 4)^{-3/2} \] *The derivative of the function \( f(t) \) is found using the power rule and chain rule of differentiation.* **(b) Find an equation for the tangent line to the graph of \( y = f(t) \) at the point \( (t, y) = (29, 6/5) \).** *Tangent line:* \[ y = -\frac{3}{125} x + \frac{237}{125} \] *This equation represents the tangent line at the specified point. The slope is calculated using the derivative \( f'(t) \), and the equation is found using the point-slope form.* --- **Additional Information:** In the provided answer section, the values for the derivative and tangent line are confirmed through a second attempt, indicated as "Attempt 2 of 2". *Note: There was an alert symbol (⚠) next to the equation of the tangent line, possibly indicating an error or a point of caution in a digital platform, which should be checked for accuracy.*
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Knowledge Booster
Angles, Arcs, and Chords and Tangents
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.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning