Problem

Find the critical points in the domain of the function $f(x)=6 x^{3}-5 x$.

Solution

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 \(\boxed{\sqrt{10}/6}\).

From Solvely APP
Source: https://solvelyapp.com/problems/33414/

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