Are First and Second Derivative Calculations for |x-a| - |x+a| Correct?

[lavenderblue]

Hey

I have been asked to find the first and second derivatives of lx-al-lx+al

I have, for the first derivative got, sign(x-a)-sign(x+a)

and for the second, i have: 2(delta)(x-a)-2(delta)(x+a)

am i right in both cases?

I also have to draw them 'schematically' how do i do this?

 

[Mark44]

Hey

I have been asked to find the first and second derivatives of lx-al-lx+al

I have, for the first derivative got, sign(x-a)-sign(x+a)

and for the second, i have: 2(delta)(x-a)-2(delta)(x+a)

am i right in both cases?

I also have to draw them 'schematically' how do i do this?

You can rewrite your function formula without the absolution values, using a piecewise definition on three intervals: (-inf, -a], (-a, a] and (a, inf).

For example, if x <= -a, |x - a| - |x + a| = -(x - a) - (-(x + a)) = -x + a + x +a = 2a.
Do the same for the other two intervals.

I don't know what "drawing them schematically" means, but a graph of the function would probably suffice.