Let f(x) be a continuous and differentiable f | vedclass

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(C) By the definition of the derivative,$f'(x) = \lim_{h 	o 0} \frac{f(x + h) - f(x)}{h}$.Given the functional equation $f(x + y) = f(x) - 3xy + f(y)

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$-3x + 7$

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(C) By the definition of the derivative,$f'(x) = \lim_{h 	o 0} \frac{f(x + h) - f(x)}{h}$.Given the functional equation $f(x + y) = f(x) - 3xy + f(y)$,we substitute $y = h$:$f(x + h) = f(x) - 3xh + f(h)$.Substituting this into the derivative definition:$f'(x) = \lim_{h 	o 0} \frac{f(x) - 3xh + f(h) - f(x)}{h}$$f'(x) = \lim_{h 	o 0} \frac{-3xh + f(h)}{h}$$f'(x) = \lim_{h 	o 0} (-3x + \frac{f(h)}{h})$.Given that $\lim_{h 	o 0} \frac{f(h)}{h} = 7$,we have:$f'(x) = -3x + 7$.

Let $f(x)$ be a continuous and differentiable function for all real numbers. If $f(x + y) = f(x) - 3xy + f(y)$ and $\lim_{h \to 0} \frac{f(h)}{h} = 7$,then the value of $f'(x)$ is:

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