Caluclus

posted by Anonymous

Find the absolute maximum and absolute minimum of f on the interval (-1,2]: f(x)=(-x^3+x^2+3x+1)/(x+1)
A. Maximum: (1, -2); Minimum: (-1, 2)
B. Maximum: (1, -2); Minimum: None
C. Maximum: None; Minimum: None
D. Maximum: None; Minimum: (-1, 2)
E. None of these

I got to my minimum and maximum but when you plug in -1 to get the ordered pair it is undefined and I'm not sure what the answer would be.

1. Reiny

f(x)=(-x^3+x^2+3x+1)/(x+1)
This factors and reduces to
f(x) = (x+1)(-x^2 + 2x + 1)/(x+1)
= -x^2 + 2x + 1 , x ≠ -1

f ' (x) = -2x +2 , for all x's except -1
-2x + 2 = 0
-2x = -2
x = 1 , which lies in your given domain of -1 to 2

so f(1) = -1 + 2 + 1 = 2
using the 2nd derivative test:
f ''(x) = -2, so we have a maximum

(1,2) is the only maximum point
looks like choice B

here is a graph of
f(x)=(-x^3+x^2+3x+1)/(x+1) from Wolfram
to verify my calculations.

http://www.wolframalpha.com/input/?i=plot+f%28x%29%3D%28-x%5E3%2Bx%5E2%2B3x%2B1%29%2F%28x%2B1%29+

Similar Questions

1. Algebra- Maximum and minimum.

I don't understand how to find the maximum and minimum. Determine whether the given quadratic function has a minimum value or maximum value. Then find the coordinates of the minimum or maximum point. 15.f(x) = -x2 + 2x - 4 20.f(x) …
2. Calculus (pleas help!!!)

Find the absolute maximum and absolute minimum values of the function f(x)=(x−2)(x−5)^3+11 on each of the indicated intervals. Enter -1000 for any absolute extrema that does not exist. (A) Interval = [1,4] Absolute maximum …
3. Calculus (pleas help!!!)

Find the absolute maximum and absolute minimum values of the function f(x)=(x−2)(x−5)^3+11 on each of the indicated intervals. Enter -1000 for any absolute extrema that does not exist. (A) Interval = [1,4] Absolute maximum …
4. Math

Can someone help me with these questions?
5. Calculus

Find the absolute maximum and absolute minimum values of the function f(x)=x^3+6x^2-63x+4 on each of the indicated variables. Enter DNE for does not exist. (A) Interval = [-8,0] Absolute maximum = Absolute minimum = (B) Interval = …
6. calculus

2) Let g(s)= t(4−t)^1/2 on the interval [0,2]. Find the absolute maximum and absolute minimum of g(t) on this interval. Enter DNE if the absolute maximum or minimum does not exist. The absolute max occurs at t= . The absolute …
7. calculus

there are no examples of this type of problem in my book so if you could help walk me through it - that would be extremely helpful. thanks ahead of time. Find the extreme values of the function on the interval and where they occur. …
8. Calculus

Find the absolute maximum and absolute minimum of f on the interval (-4, -1]: f(x)=(x^3+8x^2+19x+12)/(x+4) A. Maximum: None; Minimum: (-2, -1) B. Maximum: (-4, 3); Minimum (-1, 0) C. Maximum: (-4, 3); Minimum: (-2, -1) D. Maximum: …