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x³ - 34x + 12 ƒ(x) = x³

x³ - 34x + 12 ƒ(x) = x³

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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Find all rational zeros of f. Then use the depressed equation to find all roots of the equation f(x)=0(show your work)

The image displays a mathematical function expressed as: \[ f(x) = x^3 - 34x + 12 \] This function is a polynomial of degree three, also known as a cubic function. The general form of a cubic function is \( f(x) = ax^3 + bx^2 + cx + d \), where \( a \), \( b \), \( c \), and \( d \) are constants. In this particular function, the coefficient of \( x^3 \) is 1, the coefficient of \( x^2 \) is 0 (since it is not present), the coefficient of \( x \) is -34, and the constant term is 12. This function can be analyzed for various properties such as roots, critical points, and inflection points. The graph of this function would typically exhibit one or two turning points and might have distinct behavior at different intervals of \( x \). By investigating the derivative of the function, we could find its critical points and determine intervals of increase and decrease as well as concavity.
Transcribed Image Text:The image displays a mathematical function expressed as: \[ f(x) = x^3 - 34x + 12 \] This function is a polynomial of degree three, also known as a cubic function. The general form of a cubic function is \( f(x) = ax^3 + bx^2 + cx + d \), where \( a \), \( b \), \( c \), and \( d \) are constants. In this particular function, the coefficient of \( x^3 \) is 1, the coefficient of \( x^2 \) is 0 (since it is not present), the coefficient of \( x \) is -34, and the constant term is 12. This function can be analyzed for various properties such as roots, critical points, and inflection points. The graph of this function would typically exhibit one or two turning points and might have distinct behavior at different intervals of \( x \). By investigating the derivative of the function, we could find its critical points and determine intervals of increase and decrease as well as concavity.
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