Find the absolute extrema (both x and y coordinates) of the function on the specified domain.
Show your work by listing all critical values and showing your test and conclusions.
1. f (x) = x
4 ! 18x
2 + 1 on [!4,4]
2. f (x) = x
3 ! 3x
2 on [!1,3]
3. f (x) = x
3 ! 12x on [0,4]
4. f (x) = 1
x ! 2
on [0,1]
5. f (x) = 1
x
2 + 1
on [1,4]
6. f (x) = 1
x
2 + 1
on [!1,1]
7. f (x) = (3x + 1)
3
on [!2,1]
8. f (x) = 3
x
2 + 4
on [!2,2]
9. f (x) = 1! x
3 + x
on [0,3]
10. f (x) = x
x ! 2
on [3,5]
11. f (x) = x
x
2 + 2
on [!1,4]
12. f (x) = x
2 + 1
x
on (0,!)
13. f (x) = 2x +
6
x
on (0,10)
14. f (x) = 3x
2 ! 2 +
6
x
2 on (!5,0)
15. f (x) = x
ex on (0,3)
16. f (x) = ex
x ! 1
on (1,4)
17. f (x) = xex on (!3,2)
18. f (x) = xe
2! x2
on (!”,0)
19. f (x) = 8x
1
2 ! x on (10,20)
20. f (x) = 6x
2
3 ! 4x on (0,!)