The curve x² - 5y³ + 5x – 2y = -6 is shown in the graph below in blue. Use the graph below to draw line tangent to the curve at the point (-3,0). Submit your answer by dragging the black point such that the drawn tangent line (shown in red) matches the equation for it. Provide your answer below: (-6, 7) -10 -5 (-3,0) 10 -5 0 -5- -10 5 10
The curve x² - 5y³ + 5x – 2y = -6 is shown in the graph below in blue. Use the graph below to draw line tangent to the curve at the point (-3,0). Submit your answer by dragging the black point such that the drawn tangent line (shown in red) matches the equation for it. Provide your answer below: (-6, 7) -10 -5 (-3,0) 10 -5 0 -5- -10 5 10
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:### Tangent Line to a Curve
The curve \( x^2 - 5y^3 + 5x - 2y = -6 \) is shown in the graph below in blue. Use the graph below to draw a line tangent to the curve at the point \((-3, 0)\).
Submit your answer by dragging the black point such that the drawn tangent line (shown in red) matches the equation for it.
**Provide your answer below:**
#### Graph Description:
On the Cartesian plane, the following features are present:
1. **Curve**: The curve representing the implicit equation \( x^2 - 5y^3 + 5x - 2y = -6 \) is plotted in a blue color. This curve passes through the point \((-3, 0)\).
2. **Tangent Point**: The specific point on the curve where the tangent line is to be drawn, \((-3, 0)\), is indicated with a black dot and labeled with coordinates.
3. **Tangent Line**: A red line represents the tangent line to be adjusted by the user. The red tangent line is currently intersecting the curve at \((-3, 0)\) and extends across the graph.
4. **Interactive Point**: A movable black point is located on the red tangent line. This point can be dragged to adjust the tangent line's position. Another labeled point, \((-6, 7)\), is also given for context.
5. **Axes**: The graph includes both the x-axis and y-axis with grid lines for reference. The x-axis ranges from -10 to 10, and the y-axis ranges from -10 to 10.
Users can interact with the graph by adjusting the position of the black point to find the proper tangent line that just touches the curve at the specified point. The goal is to align the red tangent line so that it correctly represents the tangent to the curve at \((-3, 0)\).
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