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4x² Find the values of x where the tangent line is horizontal for the graph of f(x) = x + 2 A. x= -2, x=0, x= - 4 B. x=0, x= - 4 C. x=0, x= -2 D. x = -2

4x² Find the values of x where the tangent line is horizontal for the graph of f(x) = x + 2 A. x= -2, x=0, x= - 4 B. x=0, x= - 4 C. x=0, x= -2 D. x = -2

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Finding the Values of \(x\) Where the Tangent Line is Horizontal** For the graph of the function \(f(x) = \frac{4x^2}{x + 2}\), determine the values of \(x\) at which the tangent line is horizontal. ### Options: - **A.** \(x = -2\), \(x = 0\), \(x = -4\) - **B.** \(x = 0\), \(x = -4\) - **C.** \(x = 0\), \(x = -2\) - **D.** \(x = -2\) To find the points where the tangent is horizontal, set the derivative of the function, \(f'(x)\), equal to zero and solve for \(x\). Horizontal tangents occur at critical points where the slope of the tangent line is zero.
Transcribed Image Text:**Finding the Values of \(x\) Where the Tangent Line is Horizontal** For the graph of the function \(f(x) = \frac{4x^2}{x + 2}\), determine the values of \(x\) at which the tangent line is horizontal. ### Options: - **A.** \(x = -2\), \(x = 0\), \(x = -4\) - **B.** \(x = 0\), \(x = -4\) - **C.** \(x = 0\), \(x = -2\) - **D.** \(x = -2\) To find the points where the tangent is horizontal, set the derivative of the function, \(f'(x)\), equal to zero and solve for \(x\). Horizontal tangents occur at critical points where the slope of the tangent line is zero.
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