Answer:
Explanation:
To find the linearization of the function f(x) = sqrt(x) at x = a, we can use the linearization formula:
f(x) ≈ f(a) + f'(a) (x - a)
To use this formula, we first need to find the value of f(a) and f'(a). At x = a = 4, the value of f(x) is f(4) = sqrt(4) = 2. The derivative of f(x) is f'(x) = 1/(2 * sqrt(x)), so the value of f'(a) is f'(4) = 1/(2 * sqrt(4)) = 1/4.
Substituting these values into the linearization formula, we get:
f(x) ≈ 2 + 1/4 (x - 4)
This is the linearization of f(x) = sqrt(x) at x = 4. It is an approximation of the function f(x) that is valid for values of x that are close to 4.