## anonymous one year ago For what values of x does the graph of f(x) have a horizontal tangent? (Enter your answers as a comma-separated list.) f(x) = x3 + 9x2 + x + 3

1. kropot72

Is this a calculus question in your course?

2. anonymous

Yes, sorry i meant to say that.

3. anonymous

so you're looking for like... |dw:1442087496186:dw| something like that I assume..

4. anonymous

yes

5. anonymous

Did you try solving f ' (x) = 0

6. anonymous

f ' (x) = 0 3x^2 + 18x + 1 = 0 to solve this use quadratic formula

7. anonymous

i tried that and i got it wrong

8. anonymous

Just complete the square.$3x^2+18x+1=0$$3(x^2+6x)=-1$$c=\left(\frac{6}{2}\right)^2 = (3)^2=9$$3(x^2+6x+9)=-1+27$$3(x+3)^2=26$

9. anonymous

10. anonymous

Why are the 9 and 3 highlighted?

11. anonymous

My professor changed the original question and put them numbers instead

12. anonymous

ok lets finish the equation I was solving... let's find x. $3(x+3)^2=26$$x+3 = \pm \sqrt{\frac{26}{3}}$$x=-3\color{red}{\pm}\sqrt{\frac{26}{3}}$

13. anonymous

14. anonymous

Do you see what I mean?

15. anonymous

can you write it down on paper?

16. anonymous

its confusing to look at it on the computer

17. anonymous

$\boxed{\large x=-3+\sqrt{\frac{26}{3}}~,~ -3-\sqrt{\frac{26}{3}}}$

18. anonymous

What you have written is $\large x = -3-\sqrt{\frac{26}{3}}~,~ -3-\sqrt{\frac{26}{3}}$

19. anonymous

Did I do this right?

20. anonymous

Yes

21. anonymous

its still wrong :(

22. anonymous

I read over it and its still wrong

23. anonymous

disregard the {} i did put ()

24. anonymous

i got it to finally work thanks you guys