What is the absolute maximum value of the function f (x) = −x2 + 3x − 2 on the interval[1, 3]?A. 0B. 14C. −14D. −2E. 2

To find the absolute maximum value of the function f(x) = -x^2 + 3x - 2 on the interval [1, 3], we need to follow these steps:

1. Find the derivative of the function, f'(x) = -2x + 3.

2. Set the derivative equal to zero and solve for x to find critical points, -2x + 3 = 0. Solving for x gives x = 1.5.

3. Evaluate the function at the critical points and the endpoints of the interval.

   f(1) = -1^2 + 31 - 2 = 0 f(1.5) = -1.5^2 + 31.5 - 2 = -0.25 f(3) = -3^2 + 3*3 - 2 = -2

4. The maximum value of the function on the interval [1, 3] is the highest of these values, which is 0.

So, the answer is A. 0.