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