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The linearization of g(x) is g(x) = 2x - 9
The equation of a line is given as:
[tex]y - y_1 = m(x - x_1)[/tex]
The points given are:
g(4) = −1 and g ′(4) = 2
Note that the slope (m) is g ′(4) = 2
That is, m = 2
From the point g(4) = -1:
[tex]x_1=4, y_1=-1[/tex]
Substitute [tex]x_1=4, y_1=-1[/tex], and m = 2 into the equation [tex]y - y_1 = m(x - x_1)[/tex] for the linearization
y - (-1) = 2(x - 4)
y + 1 = 2x - 8
Subtract 1 from both sides
y + 1 - 1 = 2x - 8 - 1
y = 2x - 9
Therefore, the linearization of g(x) is g(x) = 2x - 9
Learn more on linearization here: https://brainly.com/question/19468438
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