Find the critical points in the domain of the function $f(x)=6 x^{3}-5 x$.
Answer
Final Answer: The critical points of the function \(f(x)=6 x^{3}-5 x\) are \(\boxed{-\sqrt{10}/6}\) and \(\boxed{\sqrt{10}/6}\).
Step 1 ：Given the function \(f(x)=6 x^{3}-5 x\), we need to find the critical points.
Step 2 ：The critical points of a function are the points where the derivative of the function is either zero or undefined.
Step 3 ：First, we find the derivative of the function \(f'(x) = 18x^{2} - 5\).
Step 4 ：Next, we set the derivative equal to zero and solve for x, which gives us \(x = -\sqrt{10}/6\) and \(x = \sqrt{10}/6\).
Step 5 ：Final Answer: The critical points of the function \(f(x)=6 x^{3}-5 x\) are \(\boxed{-\sqrt{10}/6}\) and \(\boxed{\sqrt{10}/6}\).
