Answer
$$y - 2 = 1/4(x-4)$$
Work Step by Step
To find the linearization we first need to calculate the slope by taking the derivative.
$$f'(x) = 1/2* (x^{-1/2})$$
$$f'(4) = 1/2* (4^{-1/2})=1/2*2^{-1}= 1/4$$
Then we need to find the point where the line passes through,
$$f(4) = 2$$
Using the point-slope form,
$$y - 2 = 1/4(x-4)$$
