Question

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

Answer 1

Do we get to use the derivative?

Answer 2

yup!

Answer 3

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

Answer 4

3(x+1)^2

Answer 5

the derivative is 3(x+3)^2

Answer 6

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 \(f'(x) = 2(x+3)^{2}\)?

Answer 7

wait did i get the derivative wrong

Answer 8

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?

Answer 9

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

Answer 10

Isnt it using the chain rule...maybe haha

Answer 11

?? 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?

Answer 12

so actually my question was f(x)=(x+1)^3 but thats okay haha

but im not sure it can be negative

Answer 13

idk

Answer 14

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

Answer 15

hahaha ya

Answer 16

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.

Answer 17

no

Answer 18

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

Answer 19

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

Answer 20

if x was -1
right?

Answer 21

haha im stupid at calc. sorry :(

Answer 22

tkhunny where did you go????