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 + h) = f(x) - 3xh + f(h)

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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 $f(x + h) = f(x) - 3xh + f(h)$,we substitute this into the limit expression:$f'(x) = \lim_{h 	o 0} \frac{f(x) - 3xh + f(h) - f(x)}{h}$.Simplifying the expression,we get:$f'(x) = \lim_{h 	o 0} \frac{f(h) - 3xh}{h}$.$f'(x) = \lim_{h 	o 0} \left( \frac{f(h)}{h} - 3x ight)$.Given that $\lim_{h 	o 0} \frac{f(h)}{h} = 7$,we substitute this value:$f'(x) = 7 - 3x$.

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

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