Problems

In Problems 1-36, find the unique interior critical point and determine whether it is a maximum, a minimum, or neither.

37            Find the shortest distance between the line y = 1 - 4x and the origin.

38            Find the shortest distance between the curve y = 2/x and the origin.

39            Find the minimum of the curve f (x) = x^m - mx, x > 0, where m is an integer ≥ 2.

40            Find the maximum of f(x) = x^m - mx, x < 0, where m is an odd integer ≥ 2.

In Problems 41-44, find the maximum and minimum of the given curve.