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
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcf75a45c-687d-4994-8001-f519eebb3c9c%2Fa9cdc23d-90aa-47ba-9c9d-a4114a28bb58%2Fg5qgrph_processed.png&w=3840&q=75)
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.
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