Question

if y=|x-2| then dy/dx=?. y and x intersept?

Answer 1

y'= (x - 2) / |x - 2|

Answer 2

is the function differentiable?

Answer 3

let u=x-2 and we know that |u|=sqrt(u^2)

Answer 4

what about x=2?

Answer 5

I'm not sure I follow Yifan

Answer 6

y' = 1; <2,inf]
y' = -1 <inf,2],
you can write |x-2| = sqrt((x-2)^2)

In x = 2 there is no derivative, it is not defined.

Answer 7

I see now. y' does not exist at x=2. But the derivative is still correct for other values.

Answer 8

yeah that's right

Answer 9

Yes, if you try to plot the graph of the derivative you will see a step function in x = 2

Answer 10

gogind is right. this is a step function ,dy/dx gives the slope and here for x less then 2 the slope is -1 and for greater than 2 it is 1. at x=2 the slope is not difined