Limits

show all work in neat and good handwriting and do not type it.

1.

just do 8, 14, 20In Exercises 1-22, find the open interval(s) on which the function is increasing or decreasing. 1. f(x) =x2 -6x 2. f(x) =x +8x+10 3. f(x) =-2x2+4x+3 4. f(x) = -(x2+8x+12) 5. f(x) =2x +3x2-12x 6. f(x)=x -6x2 +15 7. f(x) =x-(3-x) 8. f (x) = (x+2)2(x-1) 9. f(x) = * -5x 10. f(x) = x4-32x+4 5 11. f(x) = x3+1 12. f(x)= x3 -4 13. f (x ) = (x-1) 3 14. f (x) = (x-2)3 15. f(x) =5-|x-51 16. f(x) = |x+31-1 17. f ( x ) = x+- 18. f(x ) = X x x+1 x+3 19. f(x) = 20. f(x) = 2 -9 21. f(x) = x -2x+1 22. f(x) = x -3x -4 x+1 x -2only no. 24, 29 In Exercises 23-30, consider the function on the interval (0, 27), find the open interval(s) on which the function is increasing or decreasing. 24. f (x) = sin x cos x 23. f(x) = ~+cos x 2 25. f(x) = sinx + cos x 26. f(x) =x+2sinx 27. f (x) = cos (2x) 28. f(x) = 3sin x+ cosx sin x 29. f (x) = sin 2 x + sin x 30. f (x ) = 1+ cos xjust do : parts a and c only - Problem 2, 6, 12,In Exercises 1-22, (a) find the critical numbers of f (if any), (b) find all the extreme values (if any) (c) apply the First Derivative Test to identify all relative extrema (if any). 1. f(x)=x+3x-2 2. f ( x ) = x+- x 3. f(x) = x(1-x) 4. f (x ) = Itx 1-x 5. f(x) =2 x(x+1) 6. f(x) =x(1-x)2 7. f (x) = (1-2x)(x-1)3 8. f ( x ) = * 1+x 9. f (x) =xV/2+x 10. f(x) =x-31+/2x+11 11. f(x) = x3 +2x 3 12. f (x) = (x-1)3 (x +9 -85x