# How do you find the critical numbers of f(x)=|x+3|-1?

Jul 11, 2016

(-3,-1)

#### Explanation:

x=c is a Critical Point either where (A) f'(c) = 0 or (B) f('c) does not exist/ is not defined

if you look at the 2 versions of this you have

$f = x + 3 - 1 = x + 2$

and for when $x + 3 < 0$, you also have $f = - x - 3 - 1 = - x - 4$

the lines meet at $x + 2 = - x - 4 , x = - 3 , y = - 1$

Point (-3,-1) is an apex. The derivative immediately to the left and right are -1 and 1 respectively. but the derivative at the point (-3,-1) is not defined. that is the CP here.

plot it if in doubt