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

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

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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use the definition: the function is derivable at x=0 if \[ \large \lim_{x\to0}\frac{f(x)-f(0)}{x-0}=\lim_{x\to0}\frac{f(x)+1}{x} \]
this limit has to exist. so u now turn to one-sided limits.

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Oh yeeah, thank you so much. After you use the rules you forget the definition.
u r welcome
actually it is easier than that, although of course @helder_edwin is correct
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
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
haha thanks :) Not everyone can do it with their eyeballs ;)

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