Find an equation of a line that is tangent to the graph of f and parallel to the given line. Line Function f(x) = x³ 3x - y + 3 = 0 y = (smaller y-intercept) y = (larger y-intercept)
Find an equation of a line that is tangent to the graph of f and parallel to the given line. Line Function f(x) = x³ 3x - y + 3 = 0 y = (smaller y-intercept) y = (larger y-intercept)
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter1: Expressions And Functions
Section1.8: Interpreting Graphs Of Functions
Problem 1GP
Related questions
Question
![**Line Tangency Problem**
Find an equation of a line that is tangent to the graph of \( f \) and parallel to the given line.
**Function:**
\[ f(x) = x^3 \]
**Line:**
\[ 3x - y + 3 = 0 \]
The solutions should be found for two cases:
- **Smaller y-intercept:**
\[ y = \_\_\_\_\_ \]
- **Larger y-intercept:**
\[ y = \_\_\_\_\_ \]
In this problem, you are given a cubic function \( f(x) = x^3 \) and a linear equation \( 3x - y + 3 = 0 \). Your task is to determine the equations of the lines that are both tangent to the cubic function and parallel to the given linear equation.
Since the lines are parallel to the given line, they must have the same slope. Write the answers for the tangents with the smaller and larger y-intercepts in the provided boxes.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbba488a1-bd87-42aa-8e5a-6cda657e400a%2F63f7b5ed-e38e-4b44-9c99-714c49ae4504%2Frngouun_processed.png&w=3840&q=75)
Transcribed Image Text:**Line Tangency Problem**
Find an equation of a line that is tangent to the graph of \( f \) and parallel to the given line.
**Function:**
\[ f(x) = x^3 \]
**Line:**
\[ 3x - y + 3 = 0 \]
The solutions should be found for two cases:
- **Smaller y-intercept:**
\[ y = \_\_\_\_\_ \]
- **Larger y-intercept:**
\[ y = \_\_\_\_\_ \]
In this problem, you are given a cubic function \( f(x) = x^3 \) and a linear equation \( 3x - y + 3 = 0 \). Your task is to determine the equations of the lines that are both tangent to the cubic function and parallel to the given linear equation.
Since the lines are parallel to the given line, they must have the same slope. Write the answers for the tangents with the smaller and larger y-intercepts in the provided boxes.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning