Find the linearization l(x) of the function at a. f(x) = x^1/2, a = 4

Solution:

Given, the function f(x) = x^1/2

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) = x^1/2

f(a) = f(4) = 2

f’(x) = 1/2 x ^-½

= 1/2√x

f’(a) = f’(4) = 1/4

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

L(x) = 2 + (1/4)(x - 4)

Therefore, the linearization of f(x) = x^1/2 at a = 4 is L(x) = 2 + (1/4)(x - 4).

Find the linearization l(x) of the function at a. f(x) = x^1/2, a = 4

Summary:

The linearization of the function f(x) = x^1/2 at a=4 is L(x) = 2 + (1/4)(x - 4).