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## lilfayfay Group Title Let f be the function defined by f(x)=3x^5 - 5x^3 +2 (a) On what intervals is f increasing? (b) On what intervals is the graph of f concave upward? (c) Write the equation of each horizontal tangent line to the graph of f. one year ago one year ago

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1. Goten77 Group Title

1st derivative test?

2. lilfayfay Group Title

do first derivative test?

3. lilfayfay Group Title

@Goten77 ok for first derivative i got 15x^4 - 15x^2

4. Goten77 Group Title

k thats right now factor it

5. Goten77 Group Title

|dw:1358134355078:dw|

6. Goten77 Group Title

set each = to 0 and get critical points |dw:1358134445508:dw| but also find where x never exist.. but it always does so ignore that part

7. Goten77 Group Title

now set up the critical points to test for when its positive and negative and you use the 1st derivative when plugging in theese values|dw:1358134521331:dw| u just use values in between the numbers

8. Goten77 Group Title

so thats part a when its increasing/decreasing.... also part c is just the graphs of y = 0 , -1, +1 since those are the 3 horizontal tangents

9. Goten77 Group Title

part b is 2nd derivative test

10. Goten77 Group Title

|dw:1358134818974:dw|

11. lilfayfay Group Title

for part a.) is it (-infinity,-1) & (1,infinity)

12. Goten77 Group Title

yes

13. lilfayfay Group Title

ok for part b.) i got x=0, and $\pm \frac{ \sqrt{2} }{ 2 }$

14. Goten77 Group Title

|dw:1358135080380:dw|

15. Goten77 Group Title

|dw:1358135162509:dw| hmm you number works to...

16. lilfayfay Group Title

then i do the SDT? (Second Derivative Test)?

17. Goten77 Group Title

well there the same i meant XD

18. Goten77 Group Title

yes now you test those numbers between/around them

19. lilfayfay Group Title

ok, how do i do part c.)? o:

20. Goten77 Group Title

i told u part c

21. Goten77 Group Title

so um heres part b|dw:1358135773604:dw|

22. Goten77 Group Title

hmm the squareroot number is very small....

23. lilfayfay Group Title

for b.) did u get $(\frac{ \sqrt{2} }{ 2 }, \infty)$

24. Goten77 Group Title

oh i keep on thinking about point of inflection <.<

25. lilfayfay Group Title

|dw:1358128938034:dw| o.O

26. lilfayfay Group Title

is that drawing seem right? :\

27. Goten77 Group Title

|dw:1358136164439:dw|

28. Goten77 Group Title

yes your right... its only concave up on that last interval

29. lilfayfay Group Title

:"D

30. lilfayfay Group Title

so how do i do part c.) again sorry..

31. lilfayfay Group Title

wait so my part b.)was wrong?

32. Goten77 Group Title

so heres what the graph looks like |dw:1358136607164:dw|

33. Goten77 Group Title

aah i meant to say for part (c)

34. Goten77 Group Title

k everything is right now.... i just got part letters mixed up

35. lilfayfay Group Title

so how do ido part c.)

36. Goten77 Group Title

......u kno what i meant... that entre paragraph just now is part C

37. Goten77 Group Title

oh i said it kinda wrong earlier i meant part Cis when f(x)= -1,0,1 meaning plug those 3 values into the original function and thats when the graph has a tangent lind so then you get y= 4 y= 2 y= 0 and thats when the graph has the horizontal tangents the x values of -1,0,1 came from the 1st derivative test since those are the critical points meaning where the derivative = 0

38. lilfayfay Group Title

ah ok ty so for part c.) i got y=-2x+2

39. Goten77 Group Title

no i gave u part 2

40. Goten77 Group Title

part c*

41. lilfayfay Group Title

yeah it says write the equation

42. Goten77 Group Title

ill explain it again

43. Goten77 Group Title

k so the 1st derivative gives us critical points meaning where the slope = 0 also meaning at those points on the original graph is where it has a horizontal tangent..... so taht means the horizontal tangents are in the form of y = # and thats it so our critical points were -1 0 and 1 plug those into the original equasion and get y= 4 y= 2 y= 0 and thats it .. those are your 3 horizontal tangents

44. lilfayfay Group Title

ohso my answer waswrong x-x

45. lilfayfay Group Title

okty :P

46. lilfayfay Group Title

@Goten77 canu help me with another 2 more pls? ^^

47. Goten77 Group Title

sure