Is it normal to have two differing gradients for one point?

I have an exam tomorrow and part of it will consist of dervitives...

I was given a revision sheet and this is one of the questions:

Find the average rate of change of f(x) = x^3 - 4x^2 + x +2 from x=1 to x=4

So, I found the derivitive: f'(x) = 3x^2 + 8x + 1

Subbed in 1: f'(1) = -4

Subbed in 4: f'(4) = 17

So, average rate of change is delta y over delta x

17-(-4)/4-1

= 21/3

= 7

Therefore, average rate of change is 7...

Looked at the revision sheet answer and the answer was 2.

I realise how they've gotten it... Just subbed in the values into the original equation.

What I don't get is how there's two different averages. Am I doing something wrong? -It's a test on derivitives so it defeats the purpose if you don't work the derivitive out... Hmmm.

Which method should I use??

Help would be appreciated.