I think what u need to understand is the basic idea of CONVEX & CONCAVE functions. Just dismiss the translations in Chinese textbooks.
By def.:
a) f : D → R is a concave function if for all x1, x2 ∈ D,f (xt) ≥ tf (x1) + (1 − t)f (x2) ∀ t ∈ [0, 1].
b) f : D → R is a convex function if for all x1, x2 ∈ D,f (xt) <= tf (x1) + (1 − t)f (x2) ∀ t ∈ [0, 1].
where X is a vector.
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