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When introducing the definition of concavity, show the graph of a concave function first. Then the students might better understand the definition.
Explain the weight 0 <= t <= 1 (and 1-t): fix x and y, thus also f(x) and f(y). Now t is the variable. t f(x) + (1-t) f(y) forms the line under the graph. f(tx + (1-t)y) will follow the graph of f and will always stay above. Hence t f(x) + (1-t) f(y) <= f(tx + (1-t)y).
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The text was updated successfully, but these errors were encountered: