is:
First, we find the derivative of the function f, which is f'(x) = 6x - 4. Now, we calculate the critical points of the function. The critical points are the values of x where the derivative equals zero. So, we solve the equation f'(x) = 0 to get x = 2/3. This gives us the critical point x = 2/3 or approximately 0.67.
As we are considering the interval [0,8], we also include the endpoints 0 and 8.
We now evaluate the function f(x) at the critical points and endpoints. We have the critical point 2/3, and endpoints 0 and 8.
For x = 2/3 or approximately 0.67, the function value f(2/3) is approximately 0.67. For x = 0, the function value f(0) is 2. And for x = 8, the function value f(8) is 162.
The absolute maximum and minimum of f(x) on [0,8] will occur at the point(s) where f(x) is largest and smallest, respectively. From the calculated function values, we see that the absolute maximum of f(x) on [0,8] is 162 and it occurs at x = 8. The absolute minimum of f(x) on [0,8] is approximately 0.67, and it occurs at x = 2/3 or approximately 0.67.
So, we can say that the absolute maximum of the function f on the interval [0,8] is 162 at x = 8, and the absolute minimum of the function f on the interval [0,8] is approximately 0.67 at x = 2/3 or approximately 0.67.