A sociologist determines that a foreign-language student has learned N(t)=20t-t^2 vocabulary terms after t hours of uninterrupted study.

What is the maxmimum rate in terms per hour at which the student is learning?

Ok.. this is what I did, but the back of the book has a different answer than my final answer.

My answer: 100

Back of book: 20

My work:

N'(t)=20-2t

0=20-2t

10=t

N(10)=10(20)-10^2

=100

So, what did I do wrong?