Let f(x) be a differentiable function for all | vedclass

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(A) By the definition of the derivative, $f^{\prime}(x) = \lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}$.Given the functional equation $f(x+y) = f(x)

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$-3x+7$

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(A) By the definition of the derivative, $f^{\prime}(x) = \lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}$.Given the functional equation $f(x+y) = f(x) + f(y) - 3xy$, we substitute $y = h$ to get $f(x+h) = f(x) + f(h) - 3xh$.Substituting this into the derivative formula:$f^{\prime}(x) = \lim _{h \rightarrow 0} \frac{f(x) + f(h) - 3xh - f(x)}{h}$.Simplifying the expression:$f^{\prime}(x) = \lim _{h \rightarrow 0} \frac{f(h) - 3xh}{h} = \lim _{h \rightarrow 0} \left( \frac{f(h)}{h} - 3x \right)$.Given that $\lim _{h \rightarrow 0} \frac{f(h)}{h} = 7$, we have:$f^{\prime}(x) = 7 - 3x$.

Let $f(x)$ be a differentiable function for all $x \in R$ and $f(x+y)=f(x)+f(y)-3xy$. If $\lim _{h \rightarrow 0} \frac{f(h)}{h}=7$, then $f^{\prime}(x)=$

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