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deepthiakella1

  • 2 years ago

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

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  1. tkhunny
    • 2 years ago
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    Do we get to use the derivative?

  2. deepthiakella1
    • 2 years ago
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    yup!

  3. tkhunny
    • 2 years ago
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    All-righty, then. Show us f'(x).

  4. deepthiakella1
    • 2 years ago
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    3(x+1)^2

  5. shamil98
    • 2 years ago
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    the derivative is 3(x+3)^2

  6. tkhunny
    • 2 years ago
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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 \(f'(x) = 2(x+3)^{2}\)?

  7. deepthiakella1
    • 2 years ago
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    wait did i get the derivative wrong

  8. tkhunny
    • 2 years ago
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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?

  9. shamil98
    • 2 years ago
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    I got a question, why is 3(x+3)^2 not the derivative? o.o

  10. deepthiakella1
    • 2 years ago
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    Isnt it using the chain rule...maybe haha

  11. tkhunny
    • 2 years ago
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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?

  12. deepthiakella1
    • 2 years ago
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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

  13. deepthiakella1
    • 2 years ago
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    idk

  14. shamil98
    • 2 years ago
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    oh then the derivative is 3(x+1)^2

  15. deepthiakella1
    • 2 years ago
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    hahaha ya

  16. tkhunny
    • 2 years ago
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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.

  17. deepthiakella1
    • 2 years ago
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    no

  18. shamil98
    • 2 years ago
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    sorry, f'(x) = 3(x+1)^2 continue with your explanation :P

  19. tkhunny
    • 2 years ago
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    Can f'(x) EVER be zero (0)?

  20. deepthiakella1
    • 2 years ago
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    if x was -1 right?

  21. deepthiakella1
    • 2 years ago
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    haha im stupid at calc. sorry :(

  22. deepthiakella1
    • 2 years ago
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    tkhunny where did you go????

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