Answer:
[tex]f(x)=4x[/tex]
Explanation: According to the power rule of taking a derivative, if we have a certain function:
[tex]f(x)=Cx^n+K[/tex]
Then the derivative of the f(x) would be as follows:
[tex]\begin{gathered} \frac{df(x)}{dx}=\frac{d(Cx^n)}{dx}+\frac{d(K)}{dx}=\frac{d(Cx^n)}{dx}+0 \\ \text{ Implies }\Rightarrow\frac{d(K)}{dx}=0 \\ \therefore\Rightarrow \\ \frac{df(x)}{dx}=\frac{d(Cx^n)}{dx}=C\cdot nx^{(n-1)} \end{gathered}[/tex]
Using this rule in reverse we can calculate the antiderivative of the provided f(x) as follows:
[tex]\begin{gathered} \frac{dF(x)}{dx}=\frac{d(Cx^n)}{dx}+\frac{d(K)}{dx}=f(x)=4 \\ K=0 \\ \therefore\Rightarrow \\ \frac{dF(x)}{dx}=\frac{d(Cx^n)}{dx}=4\Rightarrow4x\Rightarrow C=4 \\ \text{ }\therefore\rightarrow \\ f(x)=4x \\ \\ \end{gathered}[/tex]
