For Exercises 1 - 3, the graph of f is shown. Find (a) the x-values where f '(x) =0, (b) the x-values where [ '(x) does not exist, (c) the intervals where f is increasing/decreasing, and (d) the x-values where any local extrema of f occur (specify the type). For Exercises 1 - 3, the graph of f is shown. Find (a) the x-values where f 0(x) = 0, (b) the x-values where ----4-...4.... f 0(x) does not exist, (c) 3. E... the intervals where f is increasing/decreasing, and (d) the x-values where any local extrema of f occur (specify the type) For Exercises 4 - 7, find (a) the partition numbers of f ' and (b) the intervals where f is increasing/decreasing. 4. f(x) = x3 -27x+4 5. f(x) = 3x4 -40x3+ 150x2 -25 6. f(x) =1x4-23-1612 3,5,9,10 and 13 7. f (x) = -3x4 - 14x3-912+6 For Exercises 8 - 1 1, find the critical value(s) of the function. 8. f(x) =x3+15x2+27x-1 9. 8(x) =x +5x4 - 35x3 10. h(1) = 1 - 212+9 11. f(x) =9x4 -22x3-30x2+50 For Exercises 12 - 16, f ' and the domain of f are given. Assuming f is continuous on its domain, find (a) the partition numbers of f', (b) the critical values of f, (c) the intervals where f is increasing/decreasing, and (d) the x-values where any local extrema of f occur using the First Derivative Test (specify the type). 12. f'(x) = (x+5)?(x-2)(x-8); domain of f is (-0o, 00) 13. f'(x) = 3x(x+4)(x-7)'; domain of f is (-co, co) 14. f'(x) = (x-1)(x+2). (x-6)4 domain of f is (-00, 6) U (6,00) 15. f'(x) = =2x(x+8)2 (x+ 1)6 domain of f is (-00, -1) U(-1, 00)For Exercises 17 - 19, find (a) the partition numbers of f ', (b) the critical values of f, (c) the intervals where f is increasing/decreasing, and (d) any local extrema of f as well as where they occur using the First Derivative Test (specify the type). 17. f(x)=x>9x%2+24x-5 18. f(x) = x> =5x*=20x>+100 19. f(x)=3x4?x316):2 For Exercises 20 - 22, the graph of f' is shown. Assuming f is continuous on its domain of (co, 00), find (a) the partition numbers of f', (b) the critical values of f, (c) the intervals where f is increasing/decreasing, and (d) the x-values where any local extrema of f occur (specify the type). 17 and 21 25. A company that sells vacuum cleaners has a weekly cost function given by C(x) = 4100 26x +0.2x> dollars, where x is the number of vacuum cleaners produced each week. (a) Determine the intervals where the cost is increasing and where it is decreasing. (b) Find the value of x in which cost is minimum. INTERMEDIATE SKILLS PRACTICE For Exercises 26 - 29, find the intervals where f is increasing/decreasing. 26. f(x) = xe' 2 7. fy= 2 25 and 27 28. f(x) = x*In(x) \" 2/3 29. f(x) = (x*-25) For Exercises 30 - 35, find the critical value(s) of the function. 30. f(x)=2In(x)-10x