For each of the following functions, Önd any local minima or maxima of the following functions, and determine if they are global extreme points on the domain where the function is deÖned.

Problem Set 4
due October 25, 2022
For each of the following functions, Önd any local minima or maxima of
the following functions, and determine if they are global extreme points on
the domain where the function is deÖned.
1. f (x) = 1 x for x 2 [0; 1]
2. f (x) = maxn
x; p
x=2
o
minn
x; p
x=2
o
3. f (x) = x
2 + 2 ln x
4. f (x) = e
x=x
5. f (x) = x
2 x + 10 for x 5
6. (Extra Credit) Are the following functions concave, convex, or neither
for x > 0?
(i) f (x) = x + x
2
(ii) f (x) = x x
2
(iii) f (x) = x ln x
(iv) f (x) = x= ln x
(v) f (x) = min fx
2