 Solution

ID: past-exam-of-the-calculus-of-variations-course-of-the-university-of-oxford/2009/1/a/i/solution

F ((1 - t) x + t y) \leq (1 - t) F (x) + tF (y) (x, y \in R^{n}, 0 \leq t \leq 1) .

Thus its value on every line segment lies below the chord joining the endpoint values.

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