I have a feeling I is correct by drawing graphs. But can't really argue rigorously. Any thoughts would be appreciated!Thank you!
2026-03-26 23:02:07.1774566127
same tangent lines
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If $x>0$, then $\frac{f(x)}x\geqslant\frac{g(x)}x$; therefore, since $f'(x)=\lim_{x\to0}\frac{f(x)}x$ and $g'(x)=\lim_{x\to0}\frac{g(x)}x$, $f'(0)\geqslant g'(0)$. But if you do the same thing with $x<0$, you deduce that $f'(0)\leqslant g'(0)$. Therefore, $f'(0)=g'(0)$.