Applied Calculus

    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,!)