Calculus Question:

Question

Find the absolute minimum and absolute maximum values of f on the given interval.

f(x) = x − ln 4x, [1/2, 2]

Absolute Max:

Absolute Min:

Answer 1

The absolute minimum is (1, -0.3863) and the absolute maximum is (2, -0.0794)

Answer 2

There's a procedure for finding the absolute min and max of a continuous function on a closed interval. Maybe you've seen it before.

Find the critical points of the function within the interval. Then evaluate the function at each of these critical points and at the endpoints of the interval. The smallest of these values is the min, the largest is the max.