Question

Find the x-values in which f(x)=abs(x+3) are differentiable(in interval notation)

Answer 1

piecewise is
f(x)=x+3, x>=-3
-x-3, x<-3

Answer 2

Well what value of x gives us a sharp turn for f

Answer 3

-3?

Answer 4

So everywhere else the function f is differentiable

Answer 5

That's what I think, yes.

Answer 6

I thought -3 was differentiable too, though.

Answer 7

Because the limit of x->-3 is 0 and exists.

Answer 8

The function f is continuous at x=-3 but not differentiable

Answer 9

That is because the left derivative doesn't equal the right derivative as we approach -3.

Answer 10

\[f'(x^-)=(-x-3)'=-1 \\ f'(x^+)=(x+3)'=1 \\ f'(x^-) \neq f'(x^+)\]

Answer 11

f looks like
f' looks like