Find the absolute maximum and minimum values of the function over the indicated interval, and indicate the \( x \)-values at which they occur. \( f(x)=8 x-6 \) \( \begin{array}{ll}\text { (A) }[0,4] & \text { (B) }[-4,2] \\ \text { (A) The absolute maximum value is } \square \text { at } x=\square \\ \text { (Use a comma to separate answers as needed.) } \\ \text { The absolute minimum value is } \square \text { at } x=\square \text {. } \\ \text { (Use a comma to separate answers as needed.) } \\ \text { (B) The absolute maximum value is } \square \text { at } \mathrm{x}=\square \text {. } \\ \text { (Use a comma to separate answers as needed.) } \\ \text { The absolute minimum value is } \square \text { at } \mathrm{x}=\square \text {. } \\ \text { (Use a comma to separate answers as needed.) }\end{array} \)

For the function \( f(x) = 8x - 6 \), we note that it is a linear function, which means it has no critical points since its derivative (which is the slope, 8) does not equal zero. Therefore, the absolute maximum and minimum can be found by evaluating the function at the endpoints of the intervals. (A) For the interval \([0, 4]\): - Evaluate \( f(0) = 8(0) - 6 = -6 \) - Evaluate \( f(4) = 8(4) - 6 = 26 \) Thus, the absolute maximum value is \( 26 \) at \( x = 4 \) and the absolute minimum value is \( -6 \) at \( x = 0 \). (B) For the interval \([-4, 2]\): - Evaluate \( f(-4) = 8(-4) - 6 = -38 \) - Evaluate \( f(2) = 8(2) - 6 = 10 \) Therefore, the absolute maximum value is \( 10 \) at \( x = 2 \) and the absolute minimum value is \( -38 \) at \( x = -4 \). **Summary:** (A) The absolute maximum value is \( 26 \) at \( x = 4 \). The absolute minimum value is \( -6 \) at \( x = 0 \). (B) The absolute maximum value is \( 10 \) at \( x = 2 \). The absolute minimum value is \( -38 \) at \( x = -4 \).