the example. In Exercises 5-8, find those values of x for which the given functi
ID: 2891326 • Letter: T
Question
the example. In Exercises 5-8, find those values of x for which the given functions are increasing and those values of x for which they are decreasing. 5, y = x2 + 2x 6. y = 2 + 27x-x3 8, y = x4-6x2 7. y=2x3 + 3x2-36x-10 In Exercises 9-12, find any local maximum or minimum points of the given functions. (These are the same fiunctions as in Exercises 5-8.) 9,y=x2 + 2x 11. y=2x3 + 3x2-36x-10, 12, y=x4-6x2 In Exercises 13-16, find the values of x for which the given function is concave up, the values of a for which it is concave down, and any points of inflection. (These are the same functions as in Exercises 5-8.) 13, y=x2 +2x 15.y=2x3 + 3x2-36x-10 16. y=x4-6x2 In Exercises 17-20, sketch the graphs of the given functions by deter- mining the appropriate information and points from the first and sec- ond derivatives (see Exercises 5-16). Use a calculator to check the graph 17. y=x2 + 2x 19. y=2x3 + 3x2-36x-10 20, y=x4-6x2 10, y=2+27x-x3 39. 14.y=2+27x-x3 18, y = 2 + 27x-x3 40. In Exercises 21-32, sketch the graphs of the given functions by deter-wal mining the appropriate information and points from the first and sec- ond derivatives. Use a calculator to check the graph. In Exercises 27-32, use the function maximum-minimum feature to check the local 42. maximum and minimum points 21, y = 12x-2x2 23, y = 2x3 + 6x2-5 25, y=x3 + 3x2 + 3x + 2 26. y=x3-12x + 12 27. y=4x3-24x2 + 36x 28. y=x(x-4)3 29, y = 4x3-3x4 + 6 31. y=x5-5x W)41. 22. y = 20 + 16x-4x2 24. y=x3-9x2 + 15x + 1 In E sec 43. 30. y 202 32. y 32x + 2 44. In Exercises 33 and 34. view the graphs of y, y, y' together on a calExplanation / Answer
7. y=2x3+3x2-36x-10
y'= 6x2+6x-36
Critical points
y'=0
6(x2+x-6)=0
(x+3)(x-2)=0
x=-3,2
y'(-4)=36
y'(0)=-6
y'(3)=36
Increasing,y' >0, (-infinity,-3)U(2,infinity)
Decreasing y'<0,(-3,2)
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.