anonymous
  • anonymous
identify the open intervals on which the function is increasing or decreasing-- f(x)=(x+3)^3
Mathematics
jamiebookeater
  • jamiebookeater
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tkhunny
  • tkhunny
Do we get to use the derivative?
anonymous
  • anonymous
yup!
tkhunny
  • tkhunny
All-righty, then. Show us f'(x).

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anonymous
  • anonymous
3(x+1)^2
shamil98
  • shamil98
the derivative is 3(x+3)^2
tkhunny
  • 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 \(f'(x) = 2(x+3)^{2}\)?
anonymous
  • anonymous
wait did i get the derivative wrong
tkhunny
  • 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?
shamil98
  • shamil98
I got a question, why is 3(x+3)^2 not the derivative? o.o
anonymous
  • anonymous
Isnt it using the chain rule...maybe haha
tkhunny
  • 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?
anonymous
  • anonymous
so actually my question was f(x)=(x+1)^3 but thats okay haha but im not sure it can be negative
anonymous
  • anonymous
idk
shamil98
  • shamil98
oh then the derivative is 3(x+1)^2
anonymous
  • anonymous
hahaha ya
tkhunny
  • 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.
anonymous
  • anonymous
no
shamil98
  • shamil98
sorry, f'(x) = 3(x+1)^2 continue with your explanation :P
tkhunny
  • tkhunny
Can f'(x) EVER be zero (0)?
anonymous
  • anonymous
if x was -1 right?
anonymous
  • anonymous
haha im stupid at calc. sorry :(
anonymous
  • anonymous
tkhunny where did you go????

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