Final answer:
To determine where a function is increasing or decreasing, plug the critical numbers into the derivative of the function and evaluate the second derivative at those critical numbers.
Step-by-step explanation:
The equation you need to plug the critical numbers into to determine where the function is increasing or decreasing is the derivative of the function. The critical numbers of a function are the values of x where the derivative is either zero or undefined. To determine whether the function is increasing or decreasing at these critical numbers, you can use the first derivative test.
If the derivative is positive at a critical number, the function is increasing at that point. If the derivative is negative at a critical number, the function is decreasing at that point.
For example, let's say you have a function f(x) and its derivative is f'(x). If you find that f'(c) = 0, where c is a critical number, you can test whether the function is increasing or decreasing at c by evaluating f''(c). If f''(c) > 0, the function is increasing at c. If f''(c) < 0, the function is decreasing at c.