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2) The graph of f(x) = 0.5x(x-4) (x - 7) is given below. 10+ m 10+ c) Find the value of L(3). Your answer does not need to rely on any previous answers. Show work

2) The graph of f(x) = 0.5x(x-4) (x - 7) is given below. 10+ m 10+ c) Find the value of L(3). Your answer does not need to rely on any previous answers. Show work

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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### Problem 2 The graph of \( f(x) = 0.5x(x - 4)(x - 7) \) is given below. #### Graph Description The graph is a cubic function, depicted in a smooth red curve. The graph shows the function crossing the horizontal axis (x-axis) at approximately x = 0, x = 4, and x = 7, indicating these are the real roots. The curve demonstrates the typical shape of a cubic function with two turning points. It rises steeply from the negative y-axis, peaks, and then descends, crossing the x-axis and forming a valley before rising again. - **Axes**: The horizontal axis ranges from -1 to 8, while the vertical axis ranges from -10 to 10. #### Problem c Find the value of \( L(3) \). Your answer does not need to rely on any previous answers. Show work.
Transcribed Image Text:### Problem 2 The graph of \( f(x) = 0.5x(x - 4)(x - 7) \) is given below. #### Graph Description The graph is a cubic function, depicted in a smooth red curve. The graph shows the function crossing the horizontal axis (x-axis) at approximately x = 0, x = 4, and x = 7, indicating these are the real roots. The curve demonstrates the typical shape of a cubic function with two turning points. It rises steeply from the negative y-axis, peaks, and then descends, crossing the x-axis and forming a valley before rising again. - **Axes**: The horizontal axis ranges from -1 to 8, while the vertical axis ranges from -10 to 10. #### Problem c Find the value of \( L(3) \). Your answer does not need to rely on any previous answers. Show work.
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Step 1

L(x) is the linear approximation of the function f(x) at a point x=a  that can be found as L(x)≈f(x)=f'(a)(x-a)+f(a)

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