3x² Find the equation of the curve that passes through the point (0, 2) and has a slope of y at any point (x, y).

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter2: Functions And Graphs
Section2.4: Writing And Graphing Equations Of Lines
Problem 79E
icon
Related questions
Question
### Problem Statement

Find the equation of the curve that passes through the point (0, 2) and has a slope of \( \frac{3x^2}{y} \) at any point \((x, y)\).

### Solution Options

- \( y = 2x^3 + 4 \)
- \( y = x^3 + 2 \)  *(Highlighted as the correct answer)*
- \( y = x^3 - 2 \)
- \( y = 2x^3 - 4 \)

In this problem, you are required to determine which equation among the given options defines a curve that satisfies both the point and the slope conditions. The equation \( y = x^3 + 2 \) is indicated as the correct solution and meets the criteria given in the problem statement.
Transcribed Image Text:### Problem Statement Find the equation of the curve that passes through the point (0, 2) and has a slope of \( \frac{3x^2}{y} \) at any point \((x, y)\). ### Solution Options - \( y = 2x^3 + 4 \) - \( y = x^3 + 2 \) *(Highlighted as the correct answer)* - \( y = x^3 - 2 \) - \( y = 2x^3 - 4 \) In this problem, you are required to determine which equation among the given options defines a curve that satisfies both the point and the slope conditions. The equation \( y = x^3 + 2 \) is indicated as the correct solution and meets the criteria given in the problem statement.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

Blurred answer
Recommended textbooks for you
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897…
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Holt Mcdougal Larson Pre-algebra: Student Edition…
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL