Find Intervals of Increase and Decrease for y = 6x² - 2

To find the intervals where the function $y = 6x^2 - 2$ is increasing or decreasing, follow these steps:

• Step 1: Differentiate the function with respect to $x$.
  The derivative of the function $y = 6x^2 - 2$ is $\frac{dy}{dx} = 12x$.
• Step 2: Find the critical points by setting the derivative equal to zero.
  $12x = 0$
• Step 3: Solve for $x$.
  The solution is $x = 0$.
• Step 4: Determine the intervals around the critical point.
  - For $x < 0$, choose a test point such as $x = -1$. Substituting into the derivative gives $12(-1) = -12$, which is negative, indicating the function is decreasing.
  - For $x > 0$, choose a test point such as $x = 1$. Substituting into the derivative gives $12(1) = 12$, which is positive, indicating the function is increasing.

Therefore, the function is decreasing for $x < 0$ and increasing for $x > 0$.

Thus, the solution is $\searrow: x < 0 \, \, \, \, \nearrow: x > 0$.