Find an equation of the tangent line to the graph of the function at the given point. (글·플) || LARCALC11 5.7.057.MI. 3 arcsin x,
Find an equation of the tangent line to the graph of the function at the given point. (글·플) || LARCALC11 5.7.057.MI. 3 arcsin x,
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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Question
5.7
![**Calculus: Tangent Line to a Function**
**Problem Statement:**
Find an equation of the tangent line to the graph of the function at the given point.
\[ y = 3 \arcsin x, \left( \frac{1}{2}, \frac{\pi}{2} \right) \]
**Question:**
\[ y = \_\_\_\_ \]
**Additional Information:**
- "Show My Work (Optional)" is provided as a feature to allow students to display their solution process.
**Explanation:**
To solve this problem, you need to find the derivative of the function \( y = 3 \arcsin x \) to determine the slope of the tangent line at the given point \(\left( \frac{1}{2}, \frac{\pi}{2} \right)\). Then, use the point-slope form of a line equation to express the tangent line.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe35298e5-10ed-452c-b18c-35d9ef29ce25%2F7881afdf-4af2-48bf-89e5-4a610f2e8c41%2Fpp3wcxa_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Calculus: Tangent Line to a Function**
**Problem Statement:**
Find an equation of the tangent line to the graph of the function at the given point.
\[ y = 3 \arcsin x, \left( \frac{1}{2}, \frac{\pi}{2} \right) \]
**Question:**
\[ y = \_\_\_\_ \]
**Additional Information:**
- "Show My Work (Optional)" is provided as a feature to allow students to display their solution process.
**Explanation:**
To solve this problem, you need to find the derivative of the function \( y = 3 \arcsin x \) to determine the slope of the tangent line at the given point \(\left( \frac{1}{2}, \frac{\pi}{2} \right)\). Then, use the point-slope form of a line equation to express the tangent line.
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