Find ƒ'(−1) if 4x( f(x))² + 4x³ƒ(x) = 0 and ƒ(−1) = −1. ƒ'(−1) =

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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**Problem Statement:**

Find \( f'(-1) \) if \( 4x(f(x))^4 + 4x^3 f(x) = 0 \) and \( f(-1) = -1 \).

**Answer Form:**

\( f'(-1) = \) [____]

**Explanation:** 

The given equation is \( 4x(f(x))^4 + 4x^3 f(x) = 0 \). We need to find the derivative \( f'(x) \) and specifically evaluate it at \( x = -1 \). The additional information provided is that \( f(-1) = -1 \).
Transcribed Image Text:**Problem Statement:** Find \( f'(-1) \) if \( 4x(f(x))^4 + 4x^3 f(x) = 0 \) and \( f(-1) = -1 \). **Answer Form:** \( f'(-1) = \) [____] **Explanation:** The given equation is \( 4x(f(x))^4 + 4x^3 f(x) = 0 \). We need to find the derivative \( f'(x) \) and specifically evaluate it at \( x = -1 \). The additional information provided is that \( f(-1) = -1 \).
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