The line tangent to the graph of g(x) = x³ – 4x + 1 at the point (2, 1) is given by the formulaL(x) = 8(x – 2) + 1.These functions are graphed below.10F1-10 Which of the following statements are true? Select all that apply.O A. The functions are approximately equal on the interval 0.5 < x < 1.0.O B. The functions are approximately equal on the interval 1.9 < < 2.1.O C. The graphs intersect at the point (2, 1).D. The functions have the same y-intercept.E. The slope of the line equals g'(2).OF. The slope of the line equals g (0).O G. None of the above are true.

Answered: The line tangent to the graph of g(x) =…

The line tangent to the graph of g(x) = x³ – 4x +1 at the point (2, 1) is given by the formula L(x) = 8(x – 2) +1. These functions are graphed below. 10 F1

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section: Chapter Questions

Problem 8T

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Question

The line tangent to the graph of g(x) = x³ – 4x + 1 at the point (2, 1) is given by the formula
L(x) = 8(x – 2) + 1.
These functions are graphed below.
10
F1
-10

Which of the following statements are true? Select all that apply.
O A. The functions are approximately equal on the interval 0.5 < x < 1.0.
O B. The functions are approximately equal on the interval 1.9 < < 2.1.
O C. The graphs intersect at the point (2, 1).
D. The functions have the same y-intercept.
E. The slope of the line equals g'(2).
OF. The slope of the line equals g (0).
O G. None of the above are true.

Expert Solution

Step 1

To select: The correct options.

Given: The function is $g (x) = x^{3} - 4 x + 1$ and the line tangent to the graph at the point (2,1) is $L (x) = 8 (x - 2) + 1$ .

Concept used:

If the line is y=mx+b then m is the slope and b is the y-intercept.

The slope of the function at x=a is g'(a).

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