Question

Find all critical points of x⁴-6X²?

Answer 1

The critical points of the function f(x) = x⁴ - 6x² are found by setting its derivative, which is 4x³ - 12x, equal to zero, resulting in the points x = 0, x = √3, and x = -√3.

Step-by-step explanation:

To find all critical points of the function f(x) = x⁴ - 6x², we need to take the derivative of the function and set it equal to zero. Let's go through the steps:

1. Find the derivative of the function: f'(x) = 4x³ - 12x.
2. Set the derivative equal to zero: 4x³ - 12x = 0.
3. Factor out the common term: 4x(x² - 3) = 0.
4. Solve for x: x = 0, x = √3, x = -√3.

Therefore, the critical points are at x = 0, x = √3, and x = -√3.