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Question 9.24
Question 9.24
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TZ
leumasic
Official
3 months ago
We have
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\begin{align*} f'(x)&=\lim_{h\to 0}\frac{f(x+h)-f(x)}{h} \\ &=\lim_{h\to 0}\frac{-f(-x-h)+f(-x)}{h} \\ &=\lim_{k\to 0}\frac{-f(-x+k)+f(-x)}{-k} \\ &=\lim_{k\to 0}\frac{f(-x+k)-f(-x)}{k} \\ &=f'(-x). \end{align*}
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