Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
6.2 & 7.2
![### Transcription for Educational Website:
---
#### Find the Indicated Derivative:
Given the function for \( z = x^2 + \frac{x^2}{1-x-5x^2} \), find \(\frac{dz}{dx}\).
- \(\frac{dz}{dx} = \frac{2x + \frac{2x - x^2}{(1-x-5x^2)^2}}\) ❌
**Need Help?**
- [Read It]
---
#### Problem [11.11 Points]
For the function \( y = \frac{x^2 + 2}{x + 8} \) at the point (3, 1), find the following. (Give exact answers. Do not round.)
(a) **The slope of the tangent line**
\(\frac{23}{121}\) ❌
(b) **The instantaneous rate of change of the function**
\(\frac{23}{121}\) ❌
---
**Explanation of Diagrams/Graphs:**
There are no diagrams or graphs included in the image. The content focuses solely on textual mathematical expressions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F60294897-fd7d-4111-a00d-99f8e17ab996%2F551269a2-4ded-47aa-91a4-426a59630733%2F1g74b0a_processed.png&w=3840&q=75)
Transcribed Image Text:### Transcription for Educational Website:
---
#### Find the Indicated Derivative:
Given the function for \( z = x^2 + \frac{x^2}{1-x-5x^2} \), find \(\frac{dz}{dx}\).
- \(\frac{dz}{dx} = \frac{2x + \frac{2x - x^2}{(1-x-5x^2)^2}}\) ❌
**Need Help?**
- [Read It]
---
#### Problem [11.11 Points]
For the function \( y = \frac{x^2 + 2}{x + 8} \) at the point (3, 1), find the following. (Give exact answers. Do not round.)
(a) **The slope of the tangent line**
\(\frac{23}{121}\) ❌
(b) **The instantaneous rate of change of the function**
\(\frac{23}{121}\) ❌
---
**Explanation of Diagrams/Graphs:**
There are no diagrams or graphs included in the image. The content focuses solely on textual mathematical expressions.
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