A linear function of the form f (x) = ax+b is both a convex and a concave function.

This follows from

Both (3) and (4) hold with equality, so f (x) = ax+b is both a convex and a concave function.

Transcribed Image Text:

f[cx' (1c)x"] = a[cx' + (1 - c)x"] + b = c(ax' + b) + (1 - c)(ax" + b) = cf(x)+(1- cf(x) + (1 c)f(x")