deepthiakella1
identify the open intervals on which the function is increasing or decreasing-- f(x)=(x+3)^3
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tkhunny
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Do we get to use the derivative?
deepthiakella1
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yup!
tkhunny
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All-righty, then. Show us f'(x).
deepthiakella1
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3(x+1)^2
shamil98
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the derivative is 3(x+3)^2
tkhunny
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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 \(f'(x) = 2(x+3)^{2}\)?
deepthiakella1
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wait did i get the derivative wrong
tkhunny
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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
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I got a question, why is 3(x+3)^2 not the derivative? o.o
deepthiakella1
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Isnt it using the chain rule...maybe haha
tkhunny
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?? 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?
deepthiakella1
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so actually my question was f(x)=(x+1)^3 but thats okay haha
but im not sure it can be negative
deepthiakella1
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idk
shamil98
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oh then the derivative is
3(x+1)^2
deepthiakella1
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hahaha ya
tkhunny
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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.
deepthiakella1
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no
shamil98
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sorry, f'(x) = 3(x+1)^2
continue with your explanation :P
tkhunny
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Can f'(x) EVER be zero (0)?
deepthiakella1
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if x was -1
right?
deepthiakella1
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haha im stupid at calc. sorry :(
deepthiakella1
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tkhunny where did you go????