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nickymarden

  • 2 years ago

Given the function... is it derivable at the point P(0,-1) ?

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  1. nickymarden
    • 2 years ago
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  2. helder_edwin
    • 2 years ago
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    use the definition: the function is derivable at x=0 if \[ \large \lim_{x\to0}\frac{f(x)-f(0)}{x-0}=\lim_{x\to0}\frac{f(x)+1}{x} \]

  3. helder_edwin
    • 2 years ago
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    this limit has to exist. so u now turn to one-sided limits.

  4. nickymarden
    • 2 years ago
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    Oh yeeah, thank you so much. After you use the rules you forget the definition.

  5. helder_edwin
    • 2 years ago
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    u r welcome

  6. satellite73
    • 2 years ago
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    actually it is easier than that, although of course @helder_edwin is correct

  7. satellite73
    • 2 years ago
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    just take the derivative of each piece, and replace \(x\) by \(0\) if you get the same answer, then yes, if you get a different answer, then no

  8. satellite73
    • 2 years ago
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    you can pretty much do it with your eyeballs first one is 3 second one is \(10x+3\)and when you replace \(x\) by 0 in both you get 3

  9. nickymarden
    • 2 years ago
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    haha thanks :) Not everyone can do it with their eyeballs ;)

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