In a psychology experiment, a person could memorizexwords inf(x) =2x²x

seconds (for0x10).

(a)

Findf'(x)

by using the definition of the derivative.

f'(x)=

(b)

Findf'(6).

f'(6)

=

Interpret it as an instantaneous rate of change in the proper units.

When 6 words have been memorized, the memorization time is increasing at a rate off'(6)words per second.

When 6 words have been memorized, the memorization time is increasing at a rate off'(6)seconds per word.

Whenf'(6)words have been memorized, the memorization time is increasing at a rate of 6 seconds per word.

When 6 words have been memorized, the memorization time is increasing at a rate of 6 words per second.

Whenf'(6)words have been memorized, the memorization time is increasing at a rate of 6 words per second.