correct.

The term convex function is used in mathematics. It is used to define an interval where the line segment between two points is above the graph, this can both be downward or upward.

Convex function on an open set has no more than one minimum. In demand it shows the elasticity is linear after some point and non linear on other points.

Consider 2 convex functions g(x) and f(x).

Using property of second derivative test we have:

g(x)'' > 0 and f(x)'' > 0.

We are interested in showing that y(x) = g(x) + f(x) is also convex.

y(x)'' = c*g(x)'' + k*f(x)'', where c and k are positive numbers (where is no convex function those coeficients after diferentiation will give you negative numbers).

Because c, g(x)'', k, f(x)'' are > 0 , we get y(x)'' also >0, hence y(x) is a convex function.

a polygon is convex