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Question
Find the derivative of f (x) = 3x at x = 2
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Solution
We have:
\[{f'(2) = \lim}_{h \to 0} \frac{f(2 + h) - f(2)}{h}\]
\[ = \lim_{h \to 0} \frac{3(2 + h) - 3(2)}{h}\]
\[ = \lim_{h \to 0} \frac{6 + 3h - 6}{h}\]
\[ = \lim_{h \to 0} \frac{3h}{h}\]
\[ = 3\]
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