Final answer:
The value of the derivative at the indicated extremum for the function f(x) = 4 - |x| is -1.
Step-by-step explanation:
To find the value of the derivative at the indicated extremum for the function f(x) = 4 - |x|, we need to find the derivative of the function and evaluate it at the x-coordinate of the extremum. Let's start by finding the derivative using the rules of differentiation.
The function f(x) = 4 - |x| can be written as f(x) = 4 - x when x >= 0 and f(x) = 4 + x when x < 0. Taking the derivative of f(x), we get f'(x) = -1 when x >= 0 and f'(x) = 1 when x < 0.
Since the extremum occurs at x = 0, we need to evaluate the derivative at x = 0. Plugging in x = 0, we get f'(0) = -1. Therefore, the value of the derivative at the indicated extremum is -1.