By using double-derivative test, we can find

To find the critical points of a function using the double-derivative test, follow these steps:

1. Find the first derivative of the function.
2. Set the first derivative equal to zero and solve for x. These values of x are the potential critical points.
3. Find the second derivative of the function.
4. Plug each potential critical point into the second derivative.
5. If the second derivative is positive at a potential critical point, then that point is a local minimum.
6. If the second derivative is negative at a potential critical point, then that point is a local maximum.
7. If the second derivative is zero at a potential critical point, then the test is inconclusive and further analysis is needed.

By following these steps, you can use the double-derivative test to determine the nature of the critical points of a function.