Find the linear approximation of the function f(x) = 4 - x at a = 0.

Solution:

Given, the function f(x) = 4 - x

We have to find the linearization L(x) of the function at a = 0.

Using the formula,

L(x) = f(a) + f’(a)(x - a)

Now,

f(x) = 4 - x

f(a) = f(0) = 4

f’(x) = -1

f’(a) = f’(0) = -1

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

L(x) = 4 + (-1)(x - 0)

Therefore, the linearization of f(x) = 4 - x at a = 0 is L(x) = 4 - x.

Find the linear approximation of the function f(x) = 4 - x at a = 0.

Summary:

The linearization of the function f(x) = 4 - x at a = 0 is L(x) = 4 - x.