Curvature of some functions. Determine the curvature of the functions below. For affine functions (which are both convex and concave), select only the ‘affine’ box. If a function is neither convex nor concave, select ‘neither’.
(a) f(x) = min{2, x, √x}, with dom f = R +
convex concave affine neither
(b) f(x) = x 3, with dom f = R
convex concave affine neither
(c) f(x, y) = p x min{y, 2}, with dom f = R2 +
convex concave affine neither
(d) f(x, y) = (√x + √y) 2, with dom f = R2 +
convex concave affine neither

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

33

step-by-step explanation: g=6

1010: 3030

is it i think