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

1. nickymarden

2. helder_edwin

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

this limit has to exist. so u now turn to one-sided limits.

4. nickymarden

Oh yeeah, thank you so much. After you use the rules you forget the definition.

5. helder_edwin

u r welcome

6. anonymous

actually it is easier than that, although of course @helder_edwin is correct

7. anonymous

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. anonymous

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

haha thanks :) Not everyone can do it with their eyeballs ;)