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

for

a) When does peak efficiency occur? What is the learning rate of peak efficiency?

b) What is f(x)?

a) Find f(0), f(25)

...but the answer is x = 10 and I don't even know where this number comes from! Plus, the critical points I found are outside the restrictions...

b)

...my question is why is there no "c" (arbitrary constant)??

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A manufacturer estimates marginal revenue to be dollars per unit when the level of production is q units. The corresponding marginal cost has been found to be 0.4q dollars per unit. If the manufacturer's profit is $2,000 when the level of population is 25 units, what is the profit when the level of production is 36 units?

...the right answer is $2265.80, what am I doing wrong?