The graph of the derivative of |x|?

Question

I have to describe the derivate of |x| in terms of domain as well as the graph of the derivative.

I assume it is f'(x)=1 so the sketch would be a line y=1 but what happens when x=0 - does the derivative have a hole in it?

Answer 1

f(x) = |x| = +x for x>0 and -x for x<0
f'(x) = +1 for x>0 and -1 for x<0
f'(0) is not defined: as the limit from the left and from the right are *not* equal. The graph jumps from -1 to +1 at that point.

Answer 2

If x >0 IxI = x and the derivative is 1
if x<0 IxI = -x and the derivative is -1
At x=0 the derivative does not exist.
F
So the sketch are two lines y=1 and y=-1 with a "hole"at zero

Answer 3

Yes, it does. And the domain is {x| x ε R\0} At 0 the derivative is undefined (althought the function is not) and a graph of f'(x) looks like -1 from -∞ to 0, and +1 from 0 to +∞.

HTH ☺

Doug

Answer 4

It is -1 for negative x, 1 for +ve x and not defined for x=0.