Final answer:
To find where the function is increasing or decreasing, critical numbers should be plugged into the first derivative of the function, f'(x). Therefore, the correct answer is: option d)) f′(x)>0
Step-by-step explanation:
To determine where a function is increasing or decreasing, you should plug the critical numbers into the option D) f′(x)>0.
If the first derivative of the function, denoted as f′(x), is greater than zero, the function is increasing at that interval.
If f′(x) is less than zero, the function is decreasing. The critical numbers, which are the values where f′(x)=0 or where the derivative does not exist, divide the domain of the function into intervals.
By testing these intervals with f′(x), you can determine the increasing or decreasing behavior of the function.