Question

Find the absolute maximum and minimum values of the function over the indicated interval, and indicate the x-values at which they occur. f(x) = 8 - 4x: [-2.3) Find the absolute maximum and minimum values of the function over the indicated interval, and indicate the x-values at which they occur. f(x)=x? -

Answer 1

The absolute maximum value of the function f(x) = 8 - 4x over the interval [-2, 3] is 16 at x = -2, and the absolute minimum value is -4 at x = 3.

Step-by-step explanation:

To find the absolute maximum and minimum values of the function f(x) = 8 - 4x over the interval [-2, 3], we need to consider the endpoints of the interval and determine whether the function has any critical points within the interval.

First, we calculate the function values at the endpoints:

• For x = -2: f(-2) = 8 - 4(-2) = 8 + 8 = 16
• For x = 3: f(3) = 8 - 4(3) = 8 - 12 = -4

Since the function is a straight line (linear function) and the interval does not include other critical points, the absolute maximum value of the function is at x = -2 and the absolute minimum value is at x = 3.

The absolute maximum value is 16 at x = -2, and the absolute minimum value is -4 at x = 3.