## anonymous one year ago which points are the best approximations of the relative maximum and minimum of the function f(x)=x^3+3x^2-9x-8

1. anonymous

theser are the answer options HELP!!

2. amoodarya

find f' find roots of f'=0 check them by f' sign table or ,sign of f'' to find out max or min

3. anonymous

find f'(x) and then equate to 0 to find the critical points

4. anonymous

then check f"(x) at each point.

5. anonymous

would it be B??

6. anonymous

i really need please pls someone

7. anonymous

we have not solved yet. you solve t and show ,we will guide you.

8. anonymous

i just dont even know where to start..

9. anonymous

differentiate with respect to x

10. anonymous

$f \prime \left( x \right)=3x^2+6x+9$equate it to zero and find values of x

11. anonymous

correction it is -9 not +9

12. anonymous

so f(x) = 9 when equated to 0??

13. anonymous

no $f \prime \left( x \right)=0~means~3x^2+6x-9=0$ divide by 3

14. anonymous

oh so x^2 + 2x - 3 = 0

15. anonymous

make factors

16. anonymous

x^2+(3-1)x-3=0 x^2+3x-1x-3=0

17. anonymous

how do u make factors

18. anonymous

3-1=-3 3*-1=-3

19. anonymous

correction 3-1=2

20. anonymous

coefficient of x^2*constant term is same as the product of two terms (made from coefficient of x)

21. anonymous

ok i still dont understand ugh

22. anonymous

coefficient of x^2=1 constant term=-3 product=1*-=-3 if the product is negative always subtract something to make the middle term here 2=3-1 product of 3*-1=-3

23. anonymous

i am leaving for sometime . i will be back to help you after 5 minutes.

24. anonymous

ok

25. anonymous

nevermind i figured it out

26. anonymous

i am here.

27. anonymous

have you found f"(x)

28. anonymous

Have you calculated critical points? $f \prime \prime \left( x \right)=6x+6$

29. anonymous

x(x+3)-1(x+3)=0 (x+3)(x-1)=0 x+3=0,x=-3 or x-1=0,x=1

30. anonymous

$f \prime \prime \left( -3 \right)=?$