math1235

MATH 10283 – Applied Calculus Name: ___________

12.3 – Absolute Extrema 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( ) = x4 !18x2 +1 on !4,4[ ]

2. f x( ) = x3 ! 3x2 on !1,3[ ]

3. f x( ) = x3 !12x on 0,4[ ]

4. f x( ) = 1

x ! 2 on 0,1[ ]

5. f x( ) = 1

x2 +1 on 1,4[ ]

6. f x( ) = 1

x2 +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( ) = 3x2 ! 2 + 6

x 2

on !5,0( )

15. f x( ) = x

e x

on 0,3( )

16. f x( ) = e x

x !1 on 1,4( )

17. f x( ) = xex on !3,2( )

18. f x( ) = xe2!x 2

on !",0( )

19. f x( ) = 8x12 ! x on 10,20( )

20. f x( ) = 6x23 ! 4x on 0,!( )