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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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**Task: Find the Second Derivative of the Function**

Given Function:
\[ f(x) = 5(2 - 7x)^4 \]

**Instructions:**
To find the second derivative, follow these steps:

1. **Differentiate the function to find the first derivative.**
2. **Differentiate the first derivative to find the second derivative.**

**Explanation of Process:**

1. **First Derivative \( f'(x) \):**
   - Apply the chain rule: Differentiate the outer part, then multiply by the derivative of the inner part.

2. **Second Derivative \( f''(x) \):**
   - Differentiate the result from the first derivative calculation.

This will be useful for understanding changes in the curvature and concavity of the function beyond its initial behavior.
Transcribed Image Text:**Task: Find the Second Derivative of the Function** Given Function: \[ f(x) = 5(2 - 7x)^4 \] **Instructions:** To find the second derivative, follow these steps: 1. **Differentiate the function to find the first derivative.** 2. **Differentiate the first derivative to find the second derivative.** **Explanation of Process:** 1. **First Derivative \( f'(x) \):** - Apply the chain rule: Differentiate the outer part, then multiply by the derivative of the inner part. 2. **Second Derivative \( f''(x) \):** - Differentiate the result from the first derivative calculation. This will be useful for understanding changes in the curvature and concavity of the function beyond its initial behavior.
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