Find the absolute maximum and minimum values of the function over the indicated interval, and indicate the \( x \)-values at which they occur. \( f(x)=8 x-4 \) \( \begin{array}{ll}\text { (A) }[0,5] & \text { (B) }[-6,5] \\ f^{\prime}(x)=8 \\ \text { (Simplify your answer.) } \\ \text { The absolute maximum value is } 36 \text { at } x=5 \\ \text { (Use a comma to separate answers as needed.) } \\ \text { The absolute minimum value is }-4 \text { at } x=0 \\ \text { (Use a comma to separate answers as needed.) } \\ \text { (B) The absolute maximum value is } \square \text { at } x=\square .\end{array} \) (Use a comma to separate answers as needed.)

In the context of the function \( f(x) = 8x - 4 \) defined over intervals, it’s important to first understand that a linear function, like this one, will either ascend or descend consistently across its domain. Thus, to find the absolute maximum and minimum values, we only need to evaluate the function at the endpoint values of the intervals. For interval (A) \([0, 5]\), the maximum occurs at \( f(5) = 36 \) and the minimum at \( f(0) = -4 \). Moving on to interval (B) \([-6, 5]\), we evaluate the endpoints as follows: \( f(-6) = 8(-6) - 4 = -52 \) and \( f(5) = 36 \). Thus, the absolute maximum value is \( 36 \) at \( x = 5 \), and the absolute minimum value is \( -52 \) at \( x = -6 \). So, for interval (B): The absolute maximum value is \( 36 \) at \( x = 5 \), and the absolute minimum value is \( -52 \) at \( x = -6 \).