Let f(x) represent the total number of items a subject has memorized x minutes after being presented with a long list of items to learn. Psychologists refer to the graph of y = f(x) as a learning curve and to f'(x) as the learning rate. The time of peak efficiency is the time when the learning rate is maximized. Suppose the learning rate is f'(x) = 0.1(10 + 12x − 0.6x²) for 0 ≤ x ≤ 25

a. When does peak efficiency occur? What is the learning rate at peak efficiency?

b. What is f(x)? You may assume that f(0) = 0.

c. What is the largest number of items memorized by the subject?