Final answer:
The function f(x) = -|x-11| has a maximum value of 0, occurring at x = 11. The function does not have a specific minimum value within the domain 0 ≤ x ≤ 20, as it decreases indefinitely. No option fully describes both the maximum and correct minimum concept, but option b) correctly identifies the maximum.
Step-by-step explanation:
For the function f(x) = -|x-11|, let's determine its maximum and minimum values. The absolute value function |x-11| is always non-negative, which means that when we take the negative of that, our function will always be non-positive (zero or negative).
To find the maximum, we set x to the value that makes the absolute value part equal to zero, because the smallest non-negative value (zero) will result in the largest (least negative or non-negative) value of f(x) when we take the negative. This occurs at x = 11. This gives us f(11) = -|11-11| = 0, so the maximum value is 0, occurring at x = 11.
As for the minimum value of f(x), there's no lower bound because the greater the difference of x from 11, the larger the positive value inside the absolute value, and the more negative f(x) becomes. Therefore, the minimum theoretically goes to negative infinity, but within the domain 0 ≤ x ≤ 20, the minimum occurs at the endpoints x = 0 and x = 20, where the absolute value is greatest. However, since the question asks specifically about a minimum value at a point, we consider only the context of the question and not the entire domain. Within this context, the question might be misunderstanding the concept, as the function does not have a specific minimum value at a point since it extends indefinitely towards negative infinity.
The correct answer is option b): The maximum value is 0, and it occurs at x = 11. The minimum value is not stated correctly in any of the options since the function f(x) can decrease without bound; however, the closest option that partially addresses the concept of the minimum value is -infinity and it doesn't occur at a specific point within our domain.