Find the absolute maximum and absolute minimum of f on 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
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.