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anonymous
 3 years ago
Given the function... is it derivable at the point P(0,1) ?
anonymous
 3 years ago
Given the function... is it derivable at the point P(0,1) ?

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helder_edwin
 3 years ago
Best ResponseYou've already chosen the best response.0use the definition: the function is derivable at x=0 if \[ \large \lim_{x\to0}\frac{f(x)f(0)}{x0}=\lim_{x\to0}\frac{f(x)+1}{x} \]

helder_edwin
 3 years ago
Best ResponseYou've already chosen the best response.0this limit has to exist. so u now turn to onesided limits.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Oh yeeah, thank you so much. After you use the rules you forget the definition.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0actually it is easier than that, although of course @helder_edwin is correct

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0just 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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0you 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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0haha thanks :) Not everyone can do it with their eyeballs ;)
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