a) Which of the following functions are convex, which are concave, and which are neither convex nor concave?
i) f (x) = |x|.
ii) f (x) = 1/ x over the region x > 0.
iii) f (x) = log (x) over the region x > 0.
iv) f (x) = e −x 2 .
v) f (x1, x2) = x1x2.
vi) f (x1, x2) = x 2 /1 + x 2 /2 .
b) Graph the feasible solution region for each of the following constraints:
Which of these regions is convex?
c) Is the function f (x1, x2) = x2 − |x1| concave?