## deepthiakella1 2 years ago identify the open intervals on which the function is increasing or decreasing-- f(x)=(x+3)^3

1. tkhunny

Do we get to use the derivative?

2. deepthiakella1

yup!

3. tkhunny

All-righty, then. Show us f'(x).

4. deepthiakella1

3(x+1)^2

5. shamil98

the derivative is 3(x+3)^2

6. tkhunny

Perfect. If you think of the right thing, the answer to the following question is really, REALLY easy. :-) Where is f'(x) negative, given that \(f'(x) = 2(x+3)^{2}\)?

7. deepthiakella1

wait did i get the derivative wrong

8. tkhunny

No, you got it. I just had a typo-spasm. The answer to my question is the same. When is f'(x) negative? Don't look at the graph. Just think on the structure. A Real Number squared. When is that negative?

9. shamil98

I got a question, why is 3(x+3)^2 not the derivative? o.o

10. deepthiakella1

Isnt it using the chain rule...maybe haha

11. tkhunny

?? Why as that? You have it. Don't let my typo confuse you. \(f(x) = (x+3)^{3}\) \(f'(x) = 3(x+3)^{2}\) Okay, now answer... When is f'(x) negative?

12. deepthiakella1

so actually my question was f(x)=(x+1)^3 but thats okay haha but im not sure it can be negative

13. deepthiakella1

idk

14. shamil98

oh then the derivative is 3(x+1)^2

15. deepthiakella1

hahaha ya

16. tkhunny

Come on. You can see it. If you start with a Real Number, and Square it, will you EVER get a negative number? The derivative is NOT \(3(x+1)^{2}\). The derivative is \(f'(x) = 3(x+1)^{2}\). Don't be afraid to write whole, complete expressions.

17. deepthiakella1

no

18. shamil98

sorry, f'(x) = 3(x+1)^2 continue with your explanation :P

19. tkhunny

Can f'(x) EVER be zero (0)?

20. deepthiakella1

if x was -1 right?

21. deepthiakella1

haha im stupid at calc. sorry :(

22. deepthiakella1

tkhunny where did you go????