If $f^{\prime}(x)=\frac{2}{x^{2}}$ then... A. $f(x)=-2 x^{-1}+C$ B. $f(x)=-4 x^{-3}+C$ C. $f(x)=-2 x^{-3}+C$ D. $f(x)=2 x^{-1}+C$

Step 1 ：The question is asking for the antiderivative of the function \(f^{\prime}(x)=\frac{2}{x^{2}}\). The antiderivative of a function is the function whose derivative is the given function. In this case, we need to find the function \(f(x)\) such that its derivative is \(f^{\prime}(x)=\frac{2}{x^{2}}\).

Step 2 ：The antiderivative of \(f^{\prime}(x)=\frac{2}{x^{2}}\) is \(-2/x\).

Step 3 ：This means that the function \(f(x)\) is \(-2/x\) plus a constant \(C\).

Step 4 ：Final Answer: The correct answer is \(\boxed{f(x)=-2 x^{-1}+C}\), which corresponds to option A.