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Is there an increasing continuous function $f\colon[0,1]\to\mathbb{R}$ such that the right upper derivative $D^+f(0)$ does not equal the right lower derivative $D_+f(0)$?

Recall: $$D^+f(0)=\limsup_{h\downarrow0}\frac{f(0+h)-f(0)}{h},\quad D_f(0)=\liminf_{h\downarrow0}\frac{f(0+h)-f(0)}{h}. $$

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