2. Consider the function f(x) = (2x³5x + 1) (3x² − 4). A. Distribute out the product of the two polynomials multiplied in the expression of f and simplify your result to find an equivalent expression for f(x). B. Compute f'(x) by applying the technique from Exercise 1A to the equivalent expression for f(x) that resulted from your computation in Part A. C. Alternatively, compute f'(x) by applying the product rule for derivatives to the original expression of function f given (in the statement of Exercise 2). Do not simplify the resulting expression. D. Now, simplify the resulting expression from Part C and compare to the result from Part B. Does it make sense that the two are equal? Why or why not?

Calculus: Early Transcendentals
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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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Please only help with answering quesitons B,C, and D.

Not A. 

2. Consider the function \( f(x) = (2x^3 - 5x + 1)(3x^2 - 4) \).

A. Distribute out the product of the two polynomials multiplied in the expression of \( f \) and simplify your result to find an equivalent expression for \( f(x) \).

B. Compute \( f'(x) \) by applying the technique from Exercise 1A to the equivalent expression for \( f(x) \) that resulted from your computation in Part A.

C. Alternatively, compute \( f'(x) \) by applying the product rule for derivatives to the original expression of function \( f \) given (in the statement of Exercise 2). Do not simplify the resulting expression.

D. Now, simplify the resulting expression from Part C and compare to the result from Part B. Does it make sense that the two are equal? Why or why not?
Transcribed Image Text:2. Consider the function \( f(x) = (2x^3 - 5x + 1)(3x^2 - 4) \). A. Distribute out the product of the two polynomials multiplied in the expression of \( f \) and simplify your result to find an equivalent expression for \( f(x) \). B. Compute \( f'(x) \) by applying the technique from Exercise 1A to the equivalent expression for \( f(x) \) that resulted from your computation in Part A. C. Alternatively, compute \( f'(x) \) by applying the product rule for derivatives to the original expression of function \( f \) given (in the statement of Exercise 2). Do not simplify the resulting expression. D. Now, simplify the resulting expression from Part C and compare to the result from Part B. Does it make sense that the two are equal? Why or why not?
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