Nice work on getting part (a) correct.
To complete part (b), we plug x = 8 into the derivative calculated for part (a)
[tex]f ' (x) = 6x - 1\\\\f ' (8) = 6*8 - 1\\\\f ' (8) = 48 - 1\\\\f ' (8) = 47\\\\[/tex]
47 goes in the box
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As for the multiple choice section, you have chosen the correct answer. It is choice C.
f ' (8) = 47 can be interpreted as "at exactly 8 words, the memorization time is increasing by exactly 47 seconds per word".
Phrased another way, it's taking 47 seconds longer to memorize another word at exactly the x = 8 word marker.
