Re: jensen for a derivative



José Carlos Santos wrote:
> The assertion
>
> f((x + y)/2) <= (f(x) + f(y))/2 for all x and all y in I
>
> is equivalent to the assertion "f is convex"; this follows from the
> fact that f is a derivative and therefore that it has the intermediate
> value property (i. e. if x and y belong to I and if c is somewhere
> betwenn f(x) and f(y), then there's some z between x and y such that
> f(z) = c).

I don't follow that why f is convex.
What role does intermediate value property play here?

.

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