Find the linearization l(x) of the function at a. f(x) = x, a = 4

Solution:

Linear approximation is also known as a tangent line or tangent in geometry means a line or plane that intersects a curve or a curved surface at exactly one point.

Given, the function f(x) = x

We have to find the linearization L(x) of the function at a = 4.

Using the formula,

L(x) = f(a) + f’(a)(x - a)

Now,

f(x) = x

f(a) = f(4) = 4

f’(x) = 1

f’(a) = f’(4) = 1

Substituting the values of f(a) and f’(a), the function becomes

L(x) = 4 + 1(x - 4)

Therefore, the linearization of f(x) = x at a = 4 is L(x) = 4 + 1(x - 4).

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Find the linearization l(x) of the function at a. f(x) = x, a = 4

Summary:

The linearization of the function f(x) = x at a = 4 is L(x) = 4 + 1(x - 4).