(1 point) Consider the function $f(x)=x^{4}-32 x^{2}+10, \quad-3 \leq x \leq 9$. This function has an absolute minimum value equal to and an absolute maximum value equal to Note: You can earn partial credit on this problem.

Step 1 ：Consider the function \(f(x)=x^{4}-32 x^{2}+10, -3 \leq x \leq 9\). This function is a quartic polynomial.

Step 2 ：To find the absolute minimum and maximum values, we need to find the critical points of the function. The critical points are the points where the derivative of the function is zero or undefined.

Step 3 ：In this case, the function is differentiable everywhere, so we just need to find where the derivative is zero. We also need to check the endpoints of the interval, -3 and 9, because the absolute minimum or maximum could occur there.

Step 4 ：The derivative of the function is \(f'(x) = 4x^{3} - 64x\).

Step 5 ：The critical points of the function are -4, 0, and 4.

Step 6 ：We also consider the endpoints of the interval, -3 and 9.

Step 7 ：So, we evaluate the function at all these points: -4, 0, 4, -3, and 9.

Step 8 ：The values of the function at these points are -246, 10, -246, -197, and 3979 respectively.

Step 9 ：From these values, we can see that the absolute minimum value of the function is -246 and the absolute maximum value is 3979.

Step 10 ：Final Answer: The absolute minimum value of the function is \(\boxed{-246}\) and the absolute maximum value is \(\boxed{3979}\).