The absolute value of x, |x|, is defined as |x| = x, x>=0; -x, x<0. If you derive this, then you will find that the derivative is 1 when x>=0, and -1 when x<0. But this means that the derivative as x approaches 0 from the left does not equal the derivative as x approaches 0 from the right, as -1=/=1. So the limit as x approaches 0 does not exist, and therefore the gradient does not exist at that point, and so |x| cannot be differentiated at x = 0.
Chat with our AI personalities
The absolute value of something is its difference from 0. Absolute value of -607=607
No. The absolute value is non-negative but, to be pedantic, that does not mean positive. The absolute value of 0 is 0 which is NOT positive.
It is the magnitude, or absolute value, of the real number.
The absolute value of the integer 21 is 21. The absolute value of something is its distance from 0.
Th absolute value of a number is its distance, regardless of direction, form 0.