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This question already has an answer here:

We are told that a function is convex only if the following inequality holds:

f(tx + (1 - t) x' , ty + (1 - t) y') ≤ tf(x, y) + (1-t) f(x', y')

for 0 ≤ t ≤ 1 and all pairs of points (x, y) and (x', y').

What does this mean geometrically?

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marked as duplicate by Namaste, A. Goodier, mlc, Raskolnikov, Ethan Bolker Mar 28 '18 at 21:34

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Draw the graph of a convex function and pick two points on the graph. The line interpolating these two points lies above the graph.

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