Thread: optimzation problem #2

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?

Originally Posted by skeske1234

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?

you've been asked to find the maximum for N'(t) , not N(t) ...

N'(t) = 20-2t

N'(t) is a maximum when t = 0

N'(0) = 20