The problem:

Find the absolute maximum and absolute minimum offon the interval (-1,2]:

f(x)= (-x^3 + x^2 + 3x +1) / (x+1)

The Answer Choices:a) Max: (1, -2) Min: (-1, 2)

b) Max: (1, -2) Min: None

c) Max: None Min: None

d) Max: None Min: (-1,2)

e) None of these

My Work:

1) I found the derivative: ( -2x^3 - 2x^2 + 2x + 2 ) / (x+1)^2

2) I set the derivative equal to zero and solved for x, getting my critical points: x=1,x=2,x=3.

3) Since the interval is between (-1,2], I crossed out x=3.

4) I plugged in my critical points: x=1 and x= 2, and my end points: x=-1 and x=2 into f(x).

5) Results: f(-1)=undefined; f(1)=(2); f(2)=1.

So how do I determine which point is the max and which point is the min?

I tried my best at solving this myself;however I feel stuck after going this much through it. Could anyone review my work and tell me what I did wrong or what I need to do next in order to find which are my max and min points?

Thank you for any answers.