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
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.