Question

Find the absolute maximum value and the absolute minimum value, if any, of the function. (If an answer does not exist, enter DNE.) f(x) = – x2 + 2x + 1 on [3, 6] maximum minimum X

Answer 1

To find the absolute maximum and minimum values of the function -x^2 + 2x + 1 on the interval [3, 6], we need to find the critical points within the interval, evaluate the function at those points and the endpoints, and determine the highest and lowest values obtained.

Step-by-step explanation:

To find the absolute maximum and minimum values of the function f(x) = -x^2 + 2x + 1 on the interval [3, 6], we first need to find the critical points of the function within the interval. We can do this by finding where the derivative of the function is equal to zero or undefined.

Next, we evaluate the function at the critical points as well as the endpoints of the interval [3, 6]. The highest value obtained is the absolute maximum value, and the lowest value obtained is the absolute minimum value.

Finally, we can conclude that the absolute maximum value of f(x) = -x^2 + 2x + 1 on the interval [3, 6] is 4, and the absolute minimum value is -2.