Answered

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Let g be a function of x such that g(4) = −1 and g ′(4) = 2. Find the linearization of g(4).

Sagot :

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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