## Christos 2 years ago f(x) = (2x +1)^3 f'(x) = 6(2x + 1)^2 f''(x) = 48x + 24 I need to know when its concave up/down increasing /decreasing and the inflection points I am new to this kind of stuff

1. rulnick

First derivative is nonnegative for all real x, so f is non-decreasing. Second derivative is everywhere matching the sign of x+1/2, so there is an inflection point at x=-1/2. The function is concave down on x<-1/2 and concave up on x>-1/2.

2. Christos

how did you find the -1/2

3. rulnick

f''(x)=0 at x=-1/2

4. Christos

Ok and something more are my derivative calculations correct? f(x) = (2x +1)^3 f'(x) = 6(2x + 1)^2

5. rulnick

Yes, all were perfect!

6. Christos

so its not decreasing that means its always increasing? Kinda what's the interval?

7. Christos

(0,infinity) increasing?

8. rulnick

non-decreasing means increasing or flat. it is flat at the inflection point, increasing everywhere else

9. rulnick

so increasing on the entire real line except at -1/2, where it is flat (deriv=0)

10. Christos

here it asks me the open interval on which f is increasing what should I put? (-inf,-1/2)U(-1/2,int) ?

11. rulnick

yes, very nicely done

12. Christos

and decreasing interval*

13. rulnick

empty set

14. Christos

like I just say "it's not decreasing anywhere" ?

15. rulnick

yes

16. Christos

Alright, thank you!

17. rulnick

welcome