f(x)= xsquared -2x
for y= absolute value of f(x) does the derivitive exist at x=0 and explain why.
f(x)=|x²-2x|
=x²-2x (-∞,0]U[2,∞)
=-(x²-2x) (0,2)
f'(x)
=2x-2 (-∞,0)U(2,∞)
=-(2x-2) (0,2)
f'(0-)=-2
f'(0+)=2
Therefore the derivative is not continuous at x=0, and therefore f'(0) does not exist.
See:
http://img683.imageshack.us/img683/654/1285202904.png