Question

On the closed interval [-0.5, 1.2], determine the absolute minimum output value of f and the absolute maximum output value of f. Label your answers appropriately.

Answer 1

To find the absolute minimum and maximum values of a function on a closed interval, we can evaluate the function at the critical points within the interval and at the endpoints of the interval. The smallest value will be the absolute minimum, and the largest value will be the absolute maximum. The process involves taking the derivative, solving for critical points, and evaluating the function.

Step-by-step explanation:

The absolute minimum output value of f on the closed interval [-0.5, 1.2] can be determined by evaluating the function at the critical points within the interval. To find the critical points, we can take the derivative of f and set it equal to zero.

1. Derive f(x): f'(x) = 0
2. Solve for x to find the critical points
3. Evaluate f(x) at the critical points within the interval [-0.5, 1.2]
4. The smallest value of f(x) will be the absolute minimum output value of f

To find the absolute maximum output value of f, we can evaluate the function at the endpoints of the interval [-0.5, 1.2] and compare the values to find the largest one.

Label:

• Absolute minimum output value of f: f(min) = (minimum value)
• Absolute maximum output value of f: f(max) = (maximum value)