Determine the maximum and minimum values of the function f(x)=-2log_(2)x on the interval [2,4]

To determine the maximum and minimum values of the function \( f(x) = -2\log_{2}x \) on the interval , we need to evaluate the function at critical points within the interval and at the endpoints.First, let's find the derivative of the function to locate any critical points: The derivative is: Setting the derivative equal to zero to find critical points: This equation has no solutions because is never zero for . Therefore, there are no critical points in the interval \((2, 4)\).Next, evaluate the function at the endpoints of the interval:1. At : 2. At : Comparing these values, we see that:- The maximum value of \(f(x)\) on is at .- The minimum value of \(f(x)\) on is at .