- #1
welatiger
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Hello;
I want to know why |x| is not differentiable at x=0.
Thanks
I want to know why |x| is not differentiable at x=0.
Thanks
welatiger said:Hello;
I want to know why |x| is not differentiable at x=0.
Thanks
symbolipoint said:The limits from the left and from the right are not equal.
Ray Vickson said:Just look at the graph of |x|.
jeppetrost said:.. What is this..
Aaah, that's a physicist's answer!
symbolipoint said:The limits from the left and from the right are not equal.
The term "differentiation" refers to the process of finding the rate of change or slope of a function at a specific point. In the case of abs(x), it involves determining the rate of change of the absolute value function at a given value of x.
The differentiation of abs(x) is unique because the absolute value function is not differentiable at x = 0. This means that the slope of the function at this point is undefined, making it unlike most other functions which are differentiable at all points.
The derivative of abs(x) is a piecewise function, where the derivative is equal to 1 for all positive values of x and -1 for all negative values of x. At x = 0, the derivative does not exist.
The derivative of abs(x) is used in various real-world applications, such as in physics to calculate velocity and acceleration, in economics to determine marginal cost and revenue, and in engineering to optimize systems and processes.
Yes, the process of differentiation can be applied to any absolute value function, not just abs(x). The same rules and concepts apply, such as the derivative being undefined at the point where the absolute value function crosses the x-axis.