Problem 15a

Given information

As per the given question ,

• The derivative   represents the rate at which performance improves

Step-by-step explanation

Psychologists are interested in learning theory study learning curves.

is learning curve , it will be varying with respect to time

  represents the rate  at which performance improves.

Usually at the beginning many simple, easily-learned sub-skills associated with the learning skill

From the above increases most  rapidly when psychologists learn in smaller interval of time.

mathematically ,  the numerator is higher only when the denominator is less .

If   increases  will be less in value , which means the performance decreased .