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3. Consider the function p(x) = (2x³ − 4x + 3)⁰. A. If f(x) = 2x³ - 4x + 3 and g(x) = x6, then function p is equal to exactly one of the following: fog or go f. Which is it? Explain. B. Thinking of function p as the appropriate composition of functions from Part A, apply the chain rule for derivatives to compute an expression for p'(x). C. Using the chain rule for the derivative computation in Part B is much more efficient than distributing out the product of the six polynomials multiplied in the original expression of f, simplifying that result, and then computing the derivative of that simplified result using the technique from Exercise 1A. Explain. (Please do not waste your time performing this beastly computation, just explain why it would be much more computationally intensive than what was done in Part B.

3. Consider the function p(x) = (2x³ − 4x + 3)⁰. A. If f(x) = 2x³ - 4x + 3 and g(x) = x6, then function p is equal to exactly one of the following: fog or go f. Which is it? Explain. B. Thinking of function p as the appropriate composition of functions from Part A, apply the chain rule for derivatives to compute an expression for p'(x). C. Using the chain rule for the derivative computation in Part B is much more efficient than distributing out the product of the six polynomials multiplied in the original expression of f, simplifying that result, and then computing the derivative of that simplified result using the technique from Exercise 1A. Explain. (Please do not waste your time performing this beastly computation, just explain why it would be much more computationally intensive than what was done in Part B.

Calculus: Early Transcendentals
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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**3. Consider the function \( p(x) = (2x^3 - 4x + 3)^6 \).** **A.** If \( f(x) = 2x^3 - 4x + 3 \) and \( g(x) = x^6 \), then function \( p \) is equal to exactly one of the following: \( f \circ g \) or \( g \circ f \). Which is it? Explain. **B.** Thinking of function \( p \) as the appropriate composition of functions from Part A, apply the chain rule for derivatives to compute an expression for \( p'(x) \). **C.** Using the chain rule for the derivative computation in Part B is much more efficient than distributing out the product of the six polynomials multiplied in the original expression of \(f\), simplifying that result, and then computing the derivative of that simplified result using the technique from Exercise 1A. Explain. (Please do not waste your time performing this beastly computation, just explain why it would be much more computationally intensive than what was done in Part B.)
Transcribed Image Text:**3. Consider the function \( p(x) = (2x^3 - 4x + 3)^6 \).** **A.** If \( f(x) = 2x^3 - 4x + 3 \) and \( g(x) = x^6 \), then function \( p \) is equal to exactly one of the following: \( f \circ g \) or \( g \circ f \). Which is it? Explain. **B.** Thinking of function \( p \) as the appropriate composition of functions from Part A, apply the chain rule for derivatives to compute an expression for \( p'(x) \). **C.** Using the chain rule for the derivative computation in Part B is much more efficient than distributing out the product of the six polynomials multiplied in the original expression of \(f\), simplifying that result, and then computing the derivative of that simplified result using the technique from Exercise 1A. Explain. (Please do not waste your time performing this beastly computation, just explain why it would be much more computationally intensive than what was done in Part B.)
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