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Let y = f(x) be the equation of a line (T), and y=g(x) the equation of a curve (C).
If g is convex on [a,b], and (T) is tangent to (C) on some point on [a,b], then f(x) $\leq$ g(x) on [a,b].
An analogous inequality can be found for concave functions.
It seems efficient to use it to prove some inequalities.
But can you formally use it, as you can for Jensen's inequality ?

M.B
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  • Check this: https://math.stackexchange.com/q/1761801/42969 or this: https://math.stackexchange.com/q/668679/42969. – Martin R Nov 18 '20 at 09:34
  • Also here: https://en.wikipedia.org/wiki/Convex_function: “A differentiable function of one variable is convex on an interval if and only if its graph lies above all of its tangents” – Martin R Nov 18 '20 at 09:36
  • @MartinR Thank you – M.B Nov 18 '20 at 10:31

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