a) Which of the following functions are convex, which are concave, and which are neither convex nor concave?

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?


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