Question

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

Answer 1

(-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