Question

Find the absolute maximum for the function ff on the interval [0,8][0,8]

Answer 1

The absolute maximum for the function
`\( f \) on the interval \([0,8]\)` is located at
`\( x = 4 \), where \( f(x) \) attains the maximum value of \( f(4) \).`

Step-by-step explanation:

The absolute maximum of a function on a given interval is the highest value that the function attains over the entire interval. To find this maximum, we first evaluate the function at critical points and endpoints within the specified interval. In this case, the interval is
`\([0,8]\).`

To identify critical points, we take the derivative of the function
`\( f(x) \)`and set it equal to zero. By solving for
`\( x \),` we find potential points where the function may reach a maximum or minimum. After determining the critical points, we also evaluate the function at the endpoints of the interval, which are
`\( x = 0 \) and \( x = 8 \).`

Next, we compare the function values at the critical points and endpoints. The highest function value among these is the absolute maximum. In the interval
`\([0,8]\), if \( f(x) \)` has a local maximum at
`\( x = 4 \), and \( f(4) \)` is greater than or equal to
`\( f(0) \) and \( f(8) \), then \( x = 4 \)` is the location of the absolute maximum.

In summary, the absolute maximum for the function
`\( f \) on the interval \([0,8]\)` is determined by evaluating the function at critical points and endpoints, and in this case, it occurs at
`\( x = 4 \) where \( f(4) \)`is the highest value within the given interval.