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Question
If f is defined by f (x) = x2, find f'(2).
Solution
Given:
We know a polynomial function is everywhere differentiable. Therefore
\[f'(2) = \lim_{h \to 0} \frac{f(2 + h) - f(2)}{h}\]
\[ \Rightarrow f'(2) = \lim_{h \to 0} \frac{(2 + h )^2 - 2^2}{h}\]
\[ \Rightarrow f'(2) = \lim_{h \to 0} \frac{(4 + h^2 + 4h) - 4}{h}\]
\[ \Rightarrow f'(2) = \lim_{h \to 0} \frac{h (h + 4)}{h}\]
\[ \Rightarrow f'(2) = 4\]
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