In problem find the derivative of the function:
f(x)=|x|
The answer to the problem set says there is no possible derivative, because when x=0 there is no way to compute the derivative.
My answer was f'(x)=x^0
When x is any number, including 0, it works just fine.
Is he wrong or am I?

Question

In problem find the derivative of the function:
f(x)=|x|
The answer to the problem set says there is no possible derivative, because when x=0 there is no way to compute the derivative.
My answer was f'(x)=x^0
When x is any number, including 0, it works just fine.
Is he wrong or am I?

blues · Answer

You are, because x^0 equals 1 for any value of x. Which would suggest that the rate of change at all points equals 1.

And this is plainly not true. When x is negative, f'(x) = -1 and when x = 0, the slope of the line segment is plainly not 1. At best you'd hope it was 0, but it isn't because there is no incredibly tiny region between the -x and x regions where the line turns. It is just that the slope is -1 on one side of it and 1 on the other, and undefined at x = 0.

anonymous · Answer

Yes, i just realized that. right after i posted the question. Thanks for the quick reply though!

anonymous · Answer

deravite doesnot exist at the edge of any curve.......in this case at x=0.