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Let $X$ be some subset of euclidean space and for the bounded function $f : X \to \mathbb{R}$ and let $f(x) = \sup f(X)$. Is the limit

$$\lim_{t \to 0} \frac{f(x+ta) - f(x)}{t}$$

if it exists guaranteed to be nonpositive?

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    Hint: Suppose $f$ is constant.2012-10-16
  • 0
    I have edited my question2012-10-16

1 Answers 1