Question

Does anyone remember how to take the derivative of the absolute value function?

Answer 1

yep; except for at the tip

Answer 2

\[f(x)=1-\left| x \right| \]
from interval -1 to 1

Answer 3

Isn't it a piecewise function?

Answer 4

f(x) = x; x>0
= -x; x</0

Answer 5

piecewise is how im used to it yes

Answer 6

Thanks, I thought so. I am doing Rolle's Theorem

Answer 7

the slope of the abs() depends on which side your on :)

Answer 8

I think it fails Rolle's Theorem

Answer 9

since the tip is a cusp; it might fail it

Answer 10

I have to show f(a)=f(b)
a=-1 b=1 endpoints of interval

Answer 11

another prospect is:

|x| = sqrt(x^2)

Answer 12

\[\frac{2x}{2\sqrt{x^2}}\]

Answer 13

yes but Rolle's Theorem states f(a)=f(b) on a closed interval [a,b] and differentiable on (a,b), I believe it fails Rolle's Theorem

Answer 14

we get 0/0 if we try .. so yeah, id agree on intuition

Answer 15

fails because you have to be able to differentiate on (a,b)

Answer 16

if we average the limit from the left and right we get 0 ;)

Answer 17

Thanks :) I think I am done with this problem.