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प्रश्न
Find the derivative of the function f defined by f (x) = mx + c at x = 0.
उत्तर
Given:
Clearly, being a polynomial function, is differentiable everywhere. Therefore the derivative of
\[f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h}\]
\[ \Rightarrow f'(x) = \lim_{h \to 0} \frac{m(x + h) + c - mx - c}{h}\]
\[ \Rightarrow f'(x) = \lim_{h \to 0} \frac{mx + mh + c - mx - c}{h}\]
\[ \Rightarrow f'(x) = \lim_{h \to 0} \frac{mh}{h} \]
\[ \Rightarrow f'(x) = m\]
Thus
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