Question

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

Answer 1

use the definition: the function is derivable at x=0 if
\[ \large \lim_{x\to0}\frac{f(x)-f(0)}{x-0}=\lim_{x\to0}\frac{f(x)+1}{x} \]

Answer 2

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

Answer 3

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

Answer 4

u r welcome

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

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